MC Cartridge suggestions for Rega RB300?

You might want to read about the counterweight upgrades available for the Rega RB300 arm, because it will improve all parts of the sound spectrum, including optimizing the bass.
I use Kerry Audio F2 Titanium Heavyweight Counterweight with positive effects that were quite obvious to all who heard either my Grado or Shure MM cartridges, both before and after. Unfortunately, the Grado is an old-timer no longer made, and the moderately priced Shure V15VxMR now out of production, with remaining stock moving up in price, though still below your price range.
I defer to others regarding your precise question about which MC design to provide best bass.
Please post which phono preamp you will be using since this helps determine perceived bass quality.

I have to say that I never noticed my 103R being lacking in bass but I was using a different arm and table so I'll take your word for it. Benz Glider comes to mind and being a decent tracker and good LF response. There is a high, medium and low output model. Probably not as detailed as the Denon but still a good performer for the money. Have you thought about a Shelter 501? Seems to be many happy owners of that cartridge out there. I haven't tried one yet.

I got the vpi jr with the 300b arm. I had the spacer and arm rewire done;---got a glider as well. 'Almost forgot when I went to the xlo 3.1 cable---big help there,as well. 'Cause phono cables matter.