The accuracy limits of most of these machine is mostly operator, not the lathe. Understanding the properties of the material you are cutting, what the cutter does based on the depth of cut and material dimensions, etc. Most of these machine (G4003, 1236T, 1340GT, etc.) will easily turn to better than 0.001" w/o much effort. With the 1340GT I easily hit 0.0005" tolerance, beyond that other factors come into play. The spindle runout on either machine is about the same, the likely hood of having some issues with the machine is more likely skewed against the G4003G. I have helped quite a few G4003 owners replace their motors and convert to 3 phase because of surface finish issues, and a number of motor failures. If they work well out of the box, then you should be good, if you have QC issues they may persist. It comes down to there is no free lunch, if a machine is cheaper, then they need to cut corners getting there. As I mentioned you can chase ones tail with the numbers and features, at the end of the day you want a good accurate machine that works. Either the G4003G, the PM-1236 or the 1236GT will fit the requirement, the Taiwanese machines are just put together nicer and work smoother in my opinion. They are all good machines.
A D1-5 spindle mount in a 1000lb machine is more marketing then function, a D1-4 will perform jut as well. As Mikey indicated, you might see a difference with a much heavier lathe and deeper cut, but it ain't going to happen with a 1000lb machine. The main reason for a larger spindle mount in these type of machines is to increase the spindle diameter, so you can see something like a 2.0" spindle diameter with a D1-5 and 2.5" on a D1-6. Get into heavier machines and it is a different story. If I recall the Monarch EE used a D1-3 mount, it was good enough for aerospace parts.
You will not want to be moving the lathe after it is setup and leveled, you are looking at using a precision level to get the ways without any twist, you are not going to want to move the machine to clean up behind it. The practical solution is to give your self 1-2 feet behind the lathe to clean up, you should not need to get to the control box once the lathe is up and running. Giving some clearance behind the lathe, you can always pop open the control door enough to get in.
People tend to overthink many things when the machine is not in front of them, get the machine and start using it and your perspectives will change (myself included when I bought my first lathe, a 1340GT). Loved the lathe, eventually moved up to a heavier machine because of an opportunity/move. The full time gunsmith that purchased it loves it, he doesn't use his other larger lathe much anymore. Buy once, cry once.