for keeping a clean no-show glue-line, we paste to the roll-shadow on the floor, then 1/4 shy for the second spread.
on long shots we strike a lightly dusted chalkline and spread to it.
For cut-up areas or any questionable area we pattern scribe (armstrong felt, armstrong scribes/dividers, and a 18" and 12" bar, with the scribes set to the exact bar width, for perfect tranrfer to the sheet good when transfering the patern to the material and cutting). We pattern all 6' goods (unless the area is free of all trim and not cut-up dimensionally. Our high end builders like the for 12 foot goods as well as all the interior finish work is done before we get there, baring paint touch up. Residential is mostly pattern scribes and commercial is a mixture.
for the long shots pre-placement and placement adjustment after glueing, we knife in opposing corners net-fit, or in the case of patterned install, we ensure opposing corners are set right and tight, then the rest automatically falls into place.
I like your idea of the push broom .. .very creative.
sometimes on a dry day on a long run the adhesives tend to set up rather quickly and you got to move fast and steady.
In pattern scribing with multiple runs, we always mark the sheet vinyl perpendicular grout lines in 2 places on each end of the pattern felt, then mark the parallel seam grout line in 4 places along the length of the seam on the pattern felt (this is a double check method to ensure it is right every time and ensures you got the right grout lines in cases of a drop-pattern), this make transfer a no brainer as well as alignment to the next run.
Seams are almost always cut on the EDGE of the grout line along the sseam edge, right before where the embossing starts to rise out of the grout joint. Some manufacturers vary though in this department.
In some larger patterned areas we reverse-roll after the scribe and transfer, lay in one wall, then spread the rest up leaving less than half to a quarter to finsih ... it is a real time saver but is situational. GREAT CARE NEEDS TO BE TAKEN HERE and you need to make the roll large so it doesn not affect the overall dimentsions too much ... rolling it to tight and you can get shrinkage in length and a little gain in width.
In other areas that are patterned and knifed in as well, sometimes it is hard to get the vinyl back up to pull back for the spread. Your 6' straight edge (something every resilient mechainc should own) can come in handy. Slide it under the vinyl at a doorway then GENTLY turn it on end, which lifts the net-cut vinyl in the air 3 inches, which willl pull away from a free wall where you can get ahold of it. Again this is situational. Always check the straight edge for burrs and sharp spots.
Other times a hook knife you can gently pry a corner or a wall up but you need to be careful not to damage the goods.
A good mechainc will always have a fine metal file for sharpening their hook knives and scriber (recess and divider scriber) pins. A real money saver and time saver, especially on inlaid goods. You fine tune your hook knife so it wiull pull straight when you gently draw it accross a paste bucket lid. You fine tune the tip by filing the left or right side and front face of the point to keep the point.. I have NEVER had a hook knife out of the box that didnt need to be fine tuned in this manner. Of course ... only armstrong hook knives will do for us

This is very important to the mechanic because an un-tuned hook knife will want to *wander* away from or into a straight edge, which can cause a mis-cut or try to skip up ontop the straight edge and possibly cause an injury to you. This *wandering* is a further pain when you are transfering intricate scibe to the vinyl and freehand-cutting along the score or indentation of the scribed markes transfered over from the felt paper onto the vinyl.
Always keep 2 buckets of water ... 1 clean for your vinyl rags and 1 for just your trowels. Nothing is more of a pet peeve to me than a messy trowel or an unprepared trowel in need of scraping and solvent to get it ready .. what a waste of freaking time ... Immediately after every spread, the trowel should be placed in the trowel bucket, then it is much easier to clean for the next run, next spread, or next job, although it should be cleaned as soon as possible, and preferrably before its needed, even if it isnt, and its in the water bucket, its a few seconds til its clean, as long as its a multi-purpose adhesive. We always keep a trowel bucket 2/3's to 3/4's full in each van, with a lide securely on it, strapped securely to the shelf system for this. Also make sure your help knows what rags are for what ... as far as i am concerned the trowel rags should never be near the finish rags.
Best finish and seaming rags I have found are a cotton polyester mix. Old tshirts are wonderful. and some socks and old undergarments. They should ALWAYS be white. 100% cotton can fray and leave little knits or balls in finished seams unexpectedly, so i try to stay away from 100% cotton. If you ahve a sewing factory near you, it is a very good place to pick up good clean white scrap material for rage. We buy boxes full of them for a very low price. What cant be used for seams are used for trowels or adhesive remvoval, and cleaning solvent uses.
Also we keep an emergency 10 gallon survival can of clean water for those jobs where they may have no water service, interrupted water services, or no electric, or interrupted electical services. Comes in handy more than you might think
We always keep a gallon jug of orange hand cleaner with pumice in the trucks too.
For VCT we strike control perpendiculars (using pythagorean triples to obtain the true perpendicular), then spread and install in segments. This varies slightly with the job size but the overall concept remains the same on each job. When installing vct first rows, you want to lose-lay them in next to each other. Not tight and not real loose. just laid into place next to each other. Then when you start running rows (usually 4 rows at a time) you want to utilize the compaction and loose lay method to ensure you are running square and true to all the surrounding times. This is where the inexperienced mechanic can have great difficulty and can end up with the need to cut rows and get corner *eyes* if they arent careful. Great care needs to be exercised to ensure its runnign square and true. If you see one row falling behind another you lay it a little looser, and if you see anotehr row gaining, then you need to compact it a little tighter than the rest, and a watchful eyes needs to keep an eye one each laid tile and its justification to the surrounding tile in both directions constantly throughout the installation process, because if you dont catch it quick, you may not be abble to correct it without the need for cut rows, which is pretty unprofessional in my opinion (don't be like an old installer I hired way back and think that cut rows are the way its supposed to be done). The first main run row is the most important. I can not stress this enough. Do not compact too much or lay them too loose on either perpendicular control line.
VCT cuts can be problems for some people .. especially hot cuts. Think of this as the poor mans pattern scribe lol. lay the piece exactly on top of the piece in front of the cut. use another of the same tile to measure and score the marks for the cut to tranfer the dimentions of the cut. You want to do this on each side of the cut to transfer the marks and move the cut piece to the next tile in front of the cut as you go around a corner or a jamb .. .connect the marks, ensureing you dont over-score or over-cut a corner. We use propane torches and heat the tile from the back until a knife with cut through the tile, but not to hot as to change the dimensional stability of the tile (dont melt or burn it). Sorry iof this didnt come out right but its kind of hard to explain without pictures.