Random thoughts. I'm guessing you're buying in the spindle assembly. Do you have an option of mounting other chucks or faceplates? A four-jaw is a serious alternative and a faceplate can cover the whacky jobs that you just can't chuck-up (I turned down a spigot on an external door handle - soft white metal, to get a smooth shank to then place a phosphor bronze sleeve over and re-cut a groove for a circlip ... stupid amount of effort for a low value item but which was otherwise impossible to replace with like for the mate I was doing this for) - could only be done on a faceplate with clamps.

To some extent that impacts the position of the rails for the bed - more need for how you currently have it with the rails all the way to the spindle, if you've a fixed chuck (plan B!!!) then you could save a little on the rail. Put another way, the rail might get in the way of the work piece, though with 125mm you may be okay with that anyway, if not you could consider a gap bed, but I think you're probably okay there.

Extra bed length?, until you run out of space for the lathe you'll never regret that. It brings in the option of a tail-stock and accurate drilling/reaming. Keep that in mind. and you might want to consider if there's any machinations required to support a tail-stock (thinking you'd likely need to overreach the rather wide cross slide - could be incorporated into the design of the tail, or by narrowing the cross slide. In amongst this consider the positioning for the feed screw - I'm guessing that you're thinking of the centre-line along the bed, under the cross-slide? (cast a slot in the granite to cater for the ball-nut), it's the logical place from a mill design but less so for a lathe where you do have to consider the thill-stock. Unless....

There's something bugging me about your design - it's simple and I can't help but think that there's scope to make the cross slide optional (harder to do if you choose to go ball-screw) - cast a couple of removable end blanks that allow you to mount short sections of rail to allow the cross slide to be slid onto and removed (think the principle of a railway turntable) - replaced with e.g. a drill/tail-stock to better exploit the available bed length without cluttering it. Of course this relies on being able to easily decouple the cross slide from any lead screw - easy with acme, less so for ball. Assuming that you're using a lead screw of course. You've not mentioned screw cutting but it's kind of the elephant in the room when it comes to lathe design. And I'm assuming that if you are considering this you're simply omitting this from the design at this stage for clarity.

I will say, however, this design is heading rapidly to a solution suited for adaptation to CNC. You have to think carefully if you want to go the route to having a manual lathe, and all of the constraints that imposes, versus a complete CNC solution which allows you to avoid some of the compromises, go full ball-screw and get a solid CNC solution.

EDIT:

Aha, didn't notice Kitwin's reply on page 2. I tend to agree.