I think the reason you don't find "closed, blind" rivets in plain mild steel is due to corrosion - if you want a closed-end rivet, you're trying to keep something IN or something OUT, and what's the point if you're open to rust?
However, for a floor pan, I'd look to get it welded rather than just leaving it to rivets. Rivets aren't the greatest thing to hold shear loads (ever seen a rivet sheared neatly in half?) and are used where shear loads are not anticipated, when a light hold is all that's needed, or when it is necessary to remove panels once in a while (for inspection/maintenance/repair.) Aircraft use them mainly because a string of rivets can be lighter than a weld, and it makes it easier to replace panels when the aerodynamic profile of the airframe is disturbed.
Since a floor pan on a unibody is structural, I'd really want to get the thing welded in, rather than just rivetting it in. If it was a roof, I'd say no problem - but there, you're just dealing with a "shear panel" that locates the top of the pillars and the roofline halo, and it doesn't bear much load. Besides, it's relatively flat. A floor pan isn't so much, and it serves to bolster most of the lower mounting points (engine, transmission, crossmembers, what-have-you,) and I'm not sure I'd want my 250# arse being held up by a dozen rivets anyhow, to be perfectly honest.
Now, I'd probably be more likely to consider it if I were to use SOLID rivets instead of "Pop" rivets - but solid rivets are a lot more work and tooling to install (and I think you'll find that most aircraft rivets are solids, rather than Pops, for good reason. A solid rivet is comparable to a light bolt in taking a shear load - mostly, because it's SOLID.)
When dealing with a stressed area, it's best to attach the patches in the manner that the original panels were stuck on - in this case, welded. Also, you are essentially correct in thinking that flexion over the years will loosen the repair - but that's going to be true with pretty much ANY rivet you want to use. That's just the nature of the beast.
Also, harder steel for "Pop" rivets may SEEM smarter, but it would end up being counter-productive. More work to expand the rivet, you see. Rivets do work harden slightly when they're Popped, but only slightly.
If you have access to Machinery's Handbook, there is a very good section on rivetted joins in there, and I highly suggest you read it if you're serious about rivetting ANYTHING. They'll go into what you should do (and why) and what you should NOT do (and why NOT.) MH may be a bit spendy - it usually runs about $90 - but it will pay for itself the first time you refer to it and the job you're doing DOES NOT fail!
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