Upgrade question. Rega RP3 or RP6.

Punk rock has lack of bass recorded. To increase bass you'll need EQ or tone controls.
Entry level Regas in general have poor bass as well.
KAB modded Technics 1200 MK 5 will humiliate most of Regas and not only with bass.
Not every phono preamp will best out built-in stage. The built-in stages presumed to be in synergy with preamp stage.

Looking at your system, the little Pioneer speakers, (which, btw, are very nice) only have a 4 inch driver, so the low bass just isn't going to be there.

Adding a subwoofer would solve this.

Either of the Regas will be a major step up from the Sony you have now. If you can afford the RP6, it is an improvement over the RP3.

RP6 with Groovetracer ref sub platter. If not, the RP3 with the Groovetracer ref subplatter will be close...

Brooks Berdan in Monrovia usually has both those models in stock and those folks are always lovely to deal with. Also Acoustic Image in studio city is a Rega dealer (with an amazing listening studio) and Elliot is a class act who specializes in turntable setup. Either of them will take care of you.

Personally, I own the RP6 with a sumiko blackbird cart. Most Rega dealers are really down on Rega's stock carts so you'll likely hear that from them. My friend bought the RP3 but our systems are so different in all other respects I couldn't really tell you the difference in sound. The RP6 I think has a different platter and also includes the outboard power supply (but you can upgrade the RP3 later to the same).

Either one is a lovely turntable that basically requires very little if no effort to operate once you have everything setup. A lot of people are down on Rega turntables because of that but I'm in the set it and forget it camp.