Have you tried a VT Bass?
The VT can make my MIJ Fender VI sound like a cross between a grinding Jazz Bass and a snarling Strat.
But best of all are the clean tones and subtle tube-ish compression which beef up a 'VI's bottom and tame pick attacks.
If you play your Hellcat VI in more of a guitar role then one of Tech 21's other [Invalid or Expired Link Removed] pedals/amp simulators might be a better fit.
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EDIT:
I forgot the reverb! IMO no 'VI's sound is complete without it!
**I like the bass-shy, bright plate reverb (mono or stereo) the
Alesis NanoVerb delivers. I've had mine for twelve years now and it still sounds good.
Another 'verb worth a test drive is the Boss/Fender collaboration, the
FRV-1 which allegedly comes close to the sound of a Fender spring reverb (this is a mono only device).
**BTW. An electric instrument can be plugged directly into the NanoVerb and its adjustable output has enough gain to drive the inputs of a mono or stereo power amp and thus it can serve as an emergency pre-amp.