If you keep the Focals +1 for the Hegel products. I would also consider Bryston amps and the higher end Parasound products. All of these brands include models with very high power output, both integrated amps and power amps, that will drive your speakers to high volume levels with ample bass. All are class AB solid state amps that represent a good value.
Have you asked your Focal dealer what amps he pairs with your speakers?
Have you tried setting up your second system in a different room? How about trying it in the same room as your primary system, a room you seem to think has good acoustics? The room does make a difference, just as speaker placement does. Such an experiment should help determine if you need new amps, if the room contributes to your perceived problem or if it really is the Focal speakers, which as others have suggested you could hook up to your primary system.
Good luck!