So my concern is, do you think the 18 1/2" wide feet will prevent the lathe from tipping over? My current one is 13" wide. What is the metal rod between the pedestals for? Are you going to slope the top, underneath the ways to help with DC/clean-up? This something I am trying to figure out, because a sloped top will affect the drawer depth and I want as much storage I can get. I am looking forward to seeing your final solution.
1. My current stand is the angle iron stand that came with the lathe. The legs are 18" apart at the bottom, tapering to 6" apart at the top. I have each leg sitting in the cup of a small 3-wheel caster. I'm careful when moving it, but even with the very small caster wheels, haven't had a problem with tippyness. That's how I came up with the width of the feet.
2. The metal rod is a "bar rail" to rest a foot on. It's something I always wished for on my current setup.
3. I unless I leave the top that the lathe sits on open in the center, like my current stand, there's nowhere for the chips to go. Even if I leave the center open, then I'd have to drop the top of the chest of drawers like you said. My plan is to vacuum the chips out from between the bed rails when they build up high enough to interfere with movement of the tool rest.
4. Details of the Chest of Drawers are not shown on the drawing, but I'll only be using 10" full extension slides. If the drawers are longer front-to-back, I'm afraid they'll interfere with the handle of the lathe tool.