Changing to PBT will NOT make your MX Red switches feel like blacks. You would need to change the springs inside the switches, which is too much of a PITA, if you ask me.
And as for gaming, IMO ABS keycaps feel better on your fingers than PBT. They feel "softer" to me. Of course, the downside is that ABS will wear out much more quickly than PBT. Even the arguably best PBT caps in the world, which are the standard ones on Realforce boards, don't feel as good to me for gaming as Cherry double-shot ABS caps do. So basically changing to PBT will prolong the life of your keycaps, but will not affect in any appreciable way, the feel of the red switches. The keyboard will "feel" different, of course after you change keycaps, but it won't feel different in the manner you are postulating.
From your original post, I would say you need a tactile bump to tell you when the key has actuated. I would therefore recommend MX Browns. If you think you need a really heavy switch with tactile bump, you'll need MX Clear, which is hard to find. I think Leopold makes an FC200-model with clears, but you'll have to find it somewhere on the internets, as it's note easily available at elitekeyboards.com. However, I can't see why you'd need such a heavy key switch. You can try blacks, of course, as there are plenty of options, but I don't think it will solve the problem that you mentioned in your OP. Blacks are just stiffer reds. So the same thing will happen with blacks, as it did with reds.