Do I go from a Primaluna HP Integrated to Schiit Freya+ and a pair of Aegir Amps?

I have the following equipment and have run the following setups:
1. Schiit Freya+ preamp > First Watt SIT-3 amp > Magico A3 speakers. 
2. PrimaLuna Dialogue HP integrated amp > Magico A3

Trying to be objective I think if you want tubes or a tube sound, I would stay with PrimaLuna. If you want that clean Class A solid state sound then the Freya/solid state setup is for you.

I’m a little concerned due to lack of experience with the Aegir as to how that will drive a 4 ohm speaker. But as was said, time and again for reasonably good quality nobody beats Schiit. But as far as upgrading on the tube side, PrimaLuna is the upgrade.  Not Schiit. 

I have the Primaluna Dialogue premium HP and have it powering some AR 308HO speakers 93db in a 15' X 18' X 10' ceiling the room is carpeted and I have wall treatments and I get plenty of bass oomph from this set up, I think you should look into some wall treatments or other correction treatments like broadband bass traps or acoustic panels.I mainly listen to blues and hard rock and sometimes I feel I have almost too much bass.

If you want bigger faster louder make sure the Prima Luna is running KT150s.

Otherwise save up enough pennies to make a real upgrade. With Forte IIIs the amp is unlikely to be a system bottleneck. I suggest you look for improvements elsewhere.

@pesky_wabbit  is on the right track with the different tubes. Have you tried different pwr amp tubes in the Primaluna? Even if you haven’t, my vote is still for the Primaluna nonetheless. It’s hand wired with top notch build quality, where the Schiit has mostly SMD components on the PCBs, not that that’s necessarily a bad thing. 
It’s your system though, and it sounds like you want something different. If you want bigger, better, faster, louder, have you thought of a couple of Schiit Vidar amps and a Freya + ?