Yeah, your distortion issues are caused by the gaps that you are trying to close. TIG is sensitive to fitment. If you get a nice tight fitment, it'll flow together like butter and it won't warp hardly at all. Those big gaps mean that there is a lot of molten metal cooling down. Cooling metal contracts, pulling on the two pieces it is joining. This results in residual stress in the frame. It can be fun cutting that apart; things will bang and pop as you start cutting your welds apart and all the stress is relieved. It is very much worth the time to make a tight fit. I always err on the far side of my line, leaving a little too much material after cutting, then I file to fit. Also, if possible, clamp the joint you are welding together. It will help the two pieces flow together nicely as well. If your weld bead is much wider than 2x the thickness of the material you are joining, then your gap is too big. Of course I'm talking about this in the theoretical, perfect world, where every joint is perfect. It's an ideal to strive for; you choose when it is beneficial to stop short.
Maybe I'm showing my prejudice, but TIG should give you better welds on thin material like this than stick will. I think your observation that stick is producing a less warped structure suggests that you are welding too cold. TIG is also cleaner, reducing the risk of damaging your lovely floors with sparks and slag.
EDIT: I re-read this and wanted to add some more up-beat input. I like what you're doing. The design is good, your joints look clean and have a good cut quality. I think you'll have a tiger by the tail when it is done with a 468 in it. I'm too lazy to calculate or look it up, is that a 030 over 454 or is it some combo of stroke and bore on something smaller? What sort of torque do you think you'll be creating your vaporized rubber with?
EDIT 2: It is 060 overbored 454 for anyone wondering, and it looks like they often make in the neighborhood of 600ft.lbs.
I don't know how you will manage all that torque out of a big cube engine. It'll be making a lot of that torque right off idle. What are you thinking your tire and wheel package will be?