There is some truth to seam welding being dangerous, and some urban myth here.
1) Anything you do to the passenger compartment to make it stronger is a good thing.
2) Don't mess with the crush ZONES. (They are generally from the strut towers outwards to the front and rear of the car.)
With this in mind, adding more mass to the floor pan under yourself is a good idea. Especially around your feet. (IN a hard impact, you don't want the tire/wheel/suspension to come in and roll the floor pan and lower part of the A post around your ankles.) It also makes the passenger compartment less likely to deform and cause you harm too.
So, to put most the "seam welding kills you" myth to bed, just don't seam weld anywhere else but the passenger compartment. If you do tie your roll cage into the car, don't go past the strut towers. (I see peope doing this all the time, they run a hoop of pipe down to the front rails behind the core support off the towers, and that is just plain STUPID as that area needs to crush in an impact.)
Same goes for foam. Infinity has used it for years, and i've seen the results. (And it's one reason I own a Q45 for my family.) They hold up very well in impacts and roll over accidents. Fill your rockers, A posts, C posts and subframes with foam. You need to use structural foam however, not construction foam. Don't get stuff that expands too much either, or you'll do a huge amount of body damage to your car. (It will blow up your rockers and take the body lines right out of your car. It can also seperate panels if your not careful. One guy I've seen added it to his rear hatch to make it stronger for his huge Subs, and it split the two parts completely. (He used construction foam too, so it has very little structual ability, so got screwed twice.)
Wait till you see the cost of structual foam. It's not cheap. You can buy it at any auto paint supply store.
On this subject, Shawn and I have spent a good deal of time discussing many ideas in other threads.'
A few ideas worth it that I remember.
1) Upper front brace from strut towers to cowl. (I'd also beef up the cowl as it seems too weak to hold up to much impact. You could tie you new cage into this if you wanted. Be careful you don't add anything that could become a "skewer" as Dr. J pointed out.)
2) Lower pan brace made from alluminum with rolled ribbs that is bolted into place closing the tunnel from about the transmission crossmember to the rear suspension cradle. This would take some fabrication skills, but you could end up with a very smooth bottem to the car, and add alot of strength for a little weight. Also the weight added is nice and low. This might take a custom oval tube exhaust setup, and some other tricks like a one piece driveshaft etc. I'd use the stock centerbearing mount as one of the atachment points as well. If you tied this into the rear subframe, so it's as wide as the car there basicly, you get the same effect the DoLuck RXB has, but better I'd think. (Your floorpan would be super strong. Heck, if you used urethane as an adheasive, it would be permanent.) Just keep in mind removal of the driveshaft would become an issue with this design. You might need to notch the pan or leave a way to remove a center panel, but nothing that could not be overcome with simple designs.
3) JIC lower brace, but going a step further. Tie into the rear of the bushings, but also into the stock cross tube in a X design.
4) Rear strut towers that triangulate back to the sides of the floor. X Design again with a top brace. If your doing a cage, just tie the strut towers into your cage.
Ultimately the best desgin would start out with a hardtop car, add a cage, tie in the towers, rockers, floorpan and braces, both front and rear cradles to a ladder type bar running under both rockers also tied into the roll cage and then foam filled areas around the passenger compartment leaving the crush zones infront of and behind the strut towers intact.
Good luck.