I would make sidearms and SMGs have a closer TTK to regular primaries- only a frame off. The point being their ease of use and better ROF will then make them worth using.

If you make their practical TTK much different to primaries, it's all anyone will use instead of a primary- see the failure of the idea in D1 that 'special should be better than primaries' and the lack of primary use that follows. Everyone would spam sidearms instead of use other guns because of the mix of both theoretical and practical TTK differences coupled with movement speed.

Along with that, optimal TTK for HCs should need 2-3, 2-3, and 1-2 crit for the ROF to kill. As you said, but IMO it should be open to 3 crits being needed to avoid an obvious HC meta outside of higher skilled lobbies. I think even with 2 crits they'd beat other guns but it would need testing.

If they increase movement speed, primary lethality must increase or the game will be even more about SMGs/last hopes. I want midrange 1v1s that end in deaths, and for HCs to be much harder to use for their utility compared to D1.