I think it’s probably not the size of the machine, mine is almost as big and does not have the issues you describe.
When I assembled the machine, I noticed quite a big difference in how easily each roller would slide on the conduit. Some were so tight that they would hold the conduit against gravity. I really thought I had left all bolts loose, but I could get all rollers to slide freely by loosening the bolts even more. By the way, I had to loosen all bolts, not just the tension bolts that are meant for adjusting the tightness. My guess is that it’s possible to tighten the bearings just far enough off center to make it too tight even when the tension bolt is completely loose. My problem, I think, was that it is difficult to judge tightness with nylocs. My nylocs gripped so well that I could not hand tighten the bolts and with a wrench, it is hard or impossible to feel when you are starting to squeeze the plastic. I cannot feel an increase in torque when it’s just snug (backing off a quarter turn after hearing the crack did not work well either). Even with all rollers sliding freely, the machine did not move very easily by hand, but there were no issues moving under power aside from a bit of noise. The good news is that there is a break-in period where things magically align themselves. Everything slides much more easily and quietly now that I have used the machine for a while.
I do not think you have one of the cables flipped. I connected and disconnected my wires a few times during assembly and accidentally flipped one of the X axis steppers after I had installed the belts. This is immediately obvious even for a small motion if you try to move the machine with the LCD, and I don’t think you could move very far without something bad happening.
I also had a wire come out of a stepper connection because of the cheaply made connectors I was using. I would definitely solder the stepper extensions if I had to redo it and have done that for one of the axes. The symptoms for a missing stepper wire were pretty violent and I immediately turned the machine off. I think there might be a danger of frying the stepper driver if only one coil is connected as it is probably still trying to supply the set current to the disconnected coil. If you can move the machine by more than a few mm, I think it is likely not a wiring problem but something mechanical. Just to be safe, I would undo the belts and try it out and turn the machine off quickly if the steppers do not sound right.
Aside from how tight the rollers are, I would double check to make sure the rails are parallel. The only other thing I can think of is to make sure there is no skew by setting the rollers at the same distance from the corners before you enable the steppers. With a large machine, it is quite easy to get several mm of misalignment. I made some mechanical end stops that clip onto the rails so all I have to do is butt up the rollers against the stops before enabling the steppers. They work so well that I am not sure if I’ll even bother to wire the dual end stops.
Ryan has designed a flexible pen holder that survives being pushed 5mm into the board by people connecting their Z axis the wrong way. Wouldn’t know about that myself, of course, but I did use that pen holder for a while before mounting the router. I can only recommend it for working out the kinks before moving on to milling.