I’m using HS-5’s with zero problems. However, I do have a sub as well. (It’s a random Yamaha sub from an entertainment system, strictly there to get some bass presence).
While I’m on the III and not a II, I also had about a week of “Man, is this really it?“ until I found IR’s that really worked for me. IR’s and your hi/lo-pass filters go a LONG way.
I’m also doing mainly metal/hard rock. This advice is given to a lot of people regularly, but watch some of Leon Todd’s videos on dialing in tones. I’m not sure if he did any for the II, but you can get the same general info/tips he’s given about the III and apply them to your II.
Really spend some time searching for some IR’s you love. Even if it’s just one, for now. Devin Townsend will even say “Find one IR and use it for everything.” (Source- the recent interview with Larry Mitchell). You’ll spend a lot less time EQ’ing and messing with knobs.
On the really hi-gain stuff I put a PEQ after the cab block and cut a lot around 4500K. There’s some nastiness around there that create this really annoying standing frequency. Also you can chop everything off under 80K on the low side (not that the HS-5’s will allow you to hear it anyway, but it’ll clean up some of the bottom end).
Stick with just an amp and a cab for now. Pick one amp you really dig and scour through all your IR’s until you find the one you love.
What’s your previous experience with the real, physical versions of a Dual Rec and a 5150? I notice a lot of people who have never actually played through them, especially regarding Mesa’s, generally have a harder time dialing them in because they’re going off what they think they should feel and sound like, not what they actually produce for sound. Mesa’s are tricky to dial in in their real world counterparts, same goes for in the AxeFX. You’ll find better tones in unexpected areas (like turning the bass all the way down and using the graphic EQ to shape it and give it the balls).
Once you hit the right IR, you’re going to say “Oh! Damn! OK! Now I get it!”. Look into finding a cheap sub to use with the HS-5’s. I don’t know what/if you have a mixer, but I run the outs of my III into 2 channels on a shitty mixer and have the sub hooked up to the mixer via the headphone out jack. If I didn’t have that sub, I might find myself in the same position you’re in as the HS-5’s don’t put out jackshit for bass. Even in the guitar-sense, where you don’t really want a ton of bass frequencies on your tone. There’s just an added 3D feeling you get with certain cabs that won’t be produced with those speakers on their own and I’ve found that’s where a lot of the ”Damn, this thing sounds amazing” comes from.