"More bass warmth" is a speaker/room/amplitude issue. All the best cartridges are very close in amplitude response striving for a flat curve from 20 Hz to 20 kHz. They are all within a dB of each other.
As far as turntables go the real issues are less noise, both internal and environmental, better interface with the record and accurate speed control. The Thorens 1600 is the next step up from Rega. It is a fabulous turntable for the money adding a good suspension for environmental isolation. Form there you are getting into the Sota Sapphire with a Schroder CB or Kuzma 4 point 9. This adds a magnetic thrust bearing for less rumble and much longer bearing life. Adding Vacuum clamping and Sota's excellent mat gives you the best record interface. Moving up to the Sota line to the Cosmos gives you incredible speed accuracy, a 1" thick aluminum chassis, a constrained layer tonearm board, and vacuum clamping. Then you are off to megabuck tables like the Dohmann Helix, Basis Inspiration, Avid Acutus and SME 30/2 and 12.