10k with iron legs- benefits (?) of adding cross-structure under chipnpan?

My new-to-me 10k gap bed 4-1/2 ft lathe is on factory cast iron legs, with factory chip pan (pan is made of moderately thick pressed sheet steel with rolled edges. I plan to do a thorough disassembly and clean (it's seen little use but is grubby) and repaint the chip pan, which is peeling everywhere. I got to thinking- I've read people's remarks about 9" SB's benefitting from being mounted on a very rigid bench top, but in my case, even though the gap bed's bed is very stout- x braces throughout the length of the bed, no separate feet and sort of bridge-like sweeping buttressed ends on the bed- on mine, the legs essentially bolt to the bed (pan in between can't add a lot of rigidity) so that the lathe's bed has to serve as the main structural component.

Would I gain accuracy and performance by making everything more rigid if I fabricated an 'in between braced but relatively flat chassis' (flat to not stack a lot of additional height into the overall assembly that the legs would bolt to, and that would be self-supporting, with the chip pan and lathe then independently bolting on top of the 'chassis'? I'll try to add some photos of the lathe. Thanks in advance!

Here is a photo of the lathe on an overhead hoist as I was unloading it when bringing it home, and also a photo at least partly showing the cross-X-bracing that runs down the length of the gap bed model's bed

My thoughts are the folks reporting improvements in performance and reduction in chatter as a result of bolting a small lathe to a heavy table, are witnessing this not because constraining both ends of the bed to an infinitely stiff body in a fixed-fixed rather than simple-simple arrangement doubles the torsion rigidity of the bed and multiplies by something like 2.4 the bending stiffness of the bed...

But rather the improvement is because they don't actually have a fixed-fixed joint at both ends and the clamp load of the bolts provides a joint that can move but with a lot of friction which acts as a really good vibration dampener.

I think making the legs more rigid would only serve to decrease the chance of the bed twisting out of alignment. If you get it level to begin with though, it's not an issue. If anything it may actually make the leveling process more complicated.

best thing IMO would be to bolt in some nice heavy angle "iron" between the legs which you could lay a nice thick chunk of wood to serve as a shelf...not only would it stiffen the whole structure but would give you storage too.

My ex-un-mentionable lathe came on a metal bench type setup, I added a 4" thick wood top, and added 2 shelves underneath, it stiffened it up quite well.

Currently adding an 8" riser to my 26 x 30 SM "bench" lathe (sorry not an SB), but would like to add some mass to the base to offset the top heaviness. I can pour riser full of a mix of cement and copper slag, or have considered just plain loose copper slag, which do you guys think would give better vibration dampening?

Thanks for the suggestions. I'd been given a long piece of rectangular steel box channel .250 wall x 2" x 6" that is rigid as heck. The 6" width of the steel 2x6 is a bit too narrow (by itself) for an 'intermediate brace' for my SB 10k, because the 10k's mount bolt centers on the ends are on 6" centers. I am thinking that I could get creative on the ends- maybe make it a dogbone sort of configuration with a long piece of the 2x6 running lengthwise down the middle, with short pieces of the 2x6, maybe 8-10" long, welded in a "T" form at both ends where the legs and lathe mount. Just wanted to get a sense of whether it was completely ridiculous overkill before 'going there' - and it sounds like it is not. Many thanks!