I don't know anything about Reflextix, however the sub-floor on your '63 would have been 5/8" plywood with +/- 3/32" VAT tiles applied before the c-channels were attached for a total just a bit under 3/4". Basically, you have three options:
1) In doing a "shell off resto", you can use 5/8" material + new VCT/linoleum and come up about right by re-installing the shell after the floor finish is installed - just like it was originally done.
2) If you are doing a "shell on resto" and replace it with 5/8" material you will be about 3/32" shy because you can't get the sub-floor + flooring wedged in under the c-channel
3) If you are doing a "shell on resto" and replace it with 3/4" material you will be about 1/32" proud but you can fit it in between the c-channel and frame (it's flexible enough when the rivets @ the c-channels are removed) then apply your floor finish up to the interior skin.
Whichever way you choose, if you are using your original panels/furniture for templates or re-using them things shift a bit and will most likely have to be adjusted or trimmed to fit - they don't just go back in the same way they came out.
We did ours "shell on" using 3/4" MARINE GRADE plywood for our new floor (marine grade does not come in 5/8") then installed the linoleum up to the skin and caulked all the way around the joint.