I had an RV-3 and I didn't like it at all. Very "digital" sounding pedal IMO.
I traded it for an FRV-1, and I love the new pedal. I've compared it side by side with my Twin Reverb and it's as good or better than the Twin (the Twin might need a little tune up!)
The FRV-1 gets plenty big and intense. It also has a tone knob -- that might help with the "warmth" you're seeking.
When you say you don't use spring reverb, do you mean that your amp has no on-board reverb, or that you don't want to use a spring reverb-like pedal? If you're not looking for a spring reverb sound, you might not like this pedal. Still, I'd recommend you give it a listen.