Hi,
Don, sorry but I respectfully disagree. Floor panel replacement can be done with the body on or off the frame. In fact, many think it's best done on the frame.
I've got a similar project on the driver's side of my TR4 (brake fluid leak!) so have researched it extensively, I've seen it done on several TR2 through TR6 cars, and will be doing the job soon myself. Since the inner body of the TR6 is so similar to my earlier car, it's pretty much the same job. (IRS chassis differences are mentioned below.)
Most often the recommendation is to replace the floor panels with the body *on* the frame, and one side at a time. Many think this to be the best way to assure everything lines up properly.
Keep in mind that these cars, by modern standards, were essentially hand-built and there is often some variation in the way body parts fit together, from one car to another. I think you'll find that any replacement panels you buy need some fine-tuning to fit.
The factory used a lot of jigs to position and hold panels and components in their proper location, while building the car. Those jigs aren't available to us, so the next best thing is to use the adjacent panels as our guide.
In fact, I'm putting the finishing touches on a newly restored frame for my car now, and - as soon as suspension brakes, fuel lines, drive train, exhaust, etc. are all installed - I will move the un-repaired body off the old frame and fit it to the new *before* doing any body work. Later, when the body tub work is completed, I'll remove and disassemble it again for stripping and painting.
You do have to be cautious welding around other parts such as the frame, fuel lines, brake lines, etc. Be very careful of grinding sparks and weld spatter, too. These can damage glass and start fires.
There are various ways to contain the heat and protect those items. But, you still might end up touching up some paint. I'd suggest using MIG rather than gas welding, and go slow with small tack or stitch welds, letting it cool and coming back to in-fill a little at a time. This will help keep from damaging surrounding parts or warping the panels themselves from over-heating.
Another thing to consider is partial-panel replacement. The rear portion of my driver's side floor is fine, so I will likely only replace the forward area, creating a welded seam across the floor under the seat. The replaecement panel I bought is the full floor area, but I'll just trash the left-over portion.
A seam might be a problem for someone looking for concours-level originality, but will be pretty well hidden under the seat and can be virtually invisible with a little work.
I agree the support brackets might be a problem, too. While you are in the area, also look carefully at the B-post base (below the door latch, behind the trim panel) and the rocker panels, as these are likely problem areas if the floors are seriously rusty from general exposure (as opposed to the brake/clutch fluid leak). Rocker panel replacements are available, B-post repairs can often be done with a fabricated patch (hidden under the interior trim).
Since yours is an IRS car, floor panel replacement is a little trickier than on my solid chassis car. When some panels are removed from an IRS car, the more flexible chassis can allow the A-post (door hinge post) to droop, in particular. Extra support might be needed before cutting out the old panel. This can be as simple as a jack and some wood blocks and/or some tack-welded temporary supports.
I suggest getting hold of some of the restoration books covering your car and looking for more info. Floor panel replacement is really a pretty common repair and is often detailed in the better books. The relatively new series from Roger Williams is one I'd recommend, although I've not read the book covering the 6-cylinder cars.