A person doesn't even have to do a perfect 1/4" seam. Whatever size seam you choose to do, just keep it consistent. The 1/4 inch seam is a carry over from the days when everything was saved. Especially during the depression. It was a saving step to get as much useful fabric in the top as possible instead of inside where it couldn't be seen.
Not pressing is also a carry over from the past. Ironing has long been a drudge task that few people wanted to do. Especially women. Ironing in the old days meant long hours of sitting or standing over a hot iron to get out stubborn wrinkles.... only to have to repeat it again next wash day. Permanent press and t-shirt knit fabric was invented so people wouldn't need to iron anymore.
Pressing fabrics for a quilt top is NOT like ironing clothes. Pressing the pieces during construction of a quilt top has the same importance as accurate cutting and sewing. It should be pleasurable to see the pieces all flat and nice. It only takes a few minutes of pressing to show you how nice the blocks are working out. Pressing a few 3 inch pieces of fabric is a whole lot different than ironing a whole basket of wrinkled pants and shirts.
Well.... since machine quilters can't always get nice flat quilt tops to work on, we must learn to work on what we are given. It's not our job to press the piecer's tops. You really don't want to know what I would charge for ironing tops..... I absolutely hate ironing. The more you hate a task, the more you should charge so people won't ask you to do it. If they still ask, at least you will get paid enough to do it. Next time I would charge more.
Ok, since the top is not pressed we need to be sure we keep it fairly even on the machine. I use a tape measure and keep the sides as even as I can as I stabilize the top. I have velcro on the very ends of the bar of my machine. I also have a piece of velcro on my tape measure.
Measuring from the end of the bar to the edge of the top I get a measurement of 37 inches. I write this on a piece of masking tape and stick it to the bar. (lost my little dry erase paper)
I do the same thing on the other end of the bar.
Measuring to the edge of the top I get 36 1/2 inch. It was 36 inches but the piecer decided to make the border wider here for some reason. (The center mark on my leaders is offset an inch.)
Each time I advance the quilt, I take another measurement on both sides. If it's off I will raise the top and work it back to the correct place. I float the tops to make this easier to do. Doing this step also prevents the hourglass figure on quilts. Hour glassing is when the top is nice and straight at the beginning but gradually goes inward at the center then back out as you get to the end. Sometimes it doesn't go back out, resulting in a very wavy border at the end. And, the top will finish narrower at the end than the beginning. I hope that's understandable?
A person doesn't need to float the tops to do this. It's my personal preference. You will need to work out how to keep the sides even on your own machine. Some have bars that can be raised and others don't.