I would agree that the first steps might be trying out a few different tubes, since you can tilt the bhc tighter and more defined with swapping things around. I’m personally not a person to ask on what’s best for that, @Hazi59 could likely give you a lot of info on what works well in the bhc (and there’s some good info on that around here somewhere too)
I will note that with all that amps I’ll mention, the gumby is weaker single ended than balanced so it’s not ideal (since a tube amp with balanced inputs is not going to happen at this price point), but it should still work well enough.
I do think that trying another amp, specifically one more on a similar level to the burson would be really worthwhile. Given what you are after, I can’t help but mention the quicksilver headphone amp, it is a budget stretch for sure, and may be hard to get at this point, but it’s absolutely worth the cost and seems really up your alley with great synergy with that headphone. Would be a nice thing to go along with the burson
The aforementioned MZ2 could potentially be an option and also something that I think is an awesome pairing with the vc, although my main reservation with that is that while bass is absolutely cleaner and tighter, it’s not as lively and a bit more restrained/reserved in comparison to something like the quicksilver, could be too much of a change than you want, but otherwise would be a very solid option imo. Would be over budget, but still possibly attainable if a good used listing comes up
One I think you’d really like might be finding a decware csp2+ or csp3, to me that’s a bottlehead crack + speedball, well, on crack lol. I think the jump in refinement and technical ability while keeping a similar signature would be the most direct upgrade from the crack while addressing your complaints
Something actually more in budget and attainable, would be actually from maple tree audio (since you are in canada) if you could get your hands on an ear+ hd ii (although that’s strangely missing from their site now) or a od300 set that is a fairly balanced sounding amp that I think would be a great option and fairly attainable given your location. Although I’ve not heard either of those directly with the verite so I can’t comment too much more on there, but I bet they would pair well. They are generally fairly balanced in signature not leaning too far one way or the other so would fit what you are looking for
I think you are on the right track with the sw51+, but yes they are hard to get now. I think a hagerman tuba is really a solid alternative in most all aspects, should also be within your native price range although don’t know how much getting it to canada would end up costing, but that’s a pretty solid amp for the verite
One more potential option would be a feliks echo, and while I personally at first don’t think it’s really what you think you are looking for, you might find it valuable as dual use for both a preamp and headphone amp. I hesitate to suggest it because it’s really not something I think of when I want more overall tightness and control, but it really was a nice combo with the zmf so I think the synergy is enough to make it work, and tube swapping it can get it tighter for sure (although not as tight as some of the aforementioned)
As @dB_Cooper mentioned, you are in sorta a tough spot when it comes to tube amps at this price point, I’d agree that swapping tubes and trying a few different pads could help and be a much more feasible fix for the time being until you can save up and get something a bit higher tier if you can’t stretch for some of the above
Personally in terms of priority for what you want, I think the quicksilver, csp3/2+, and mz2 would really be my frontrunners of what to go for if possible, if not though I think grabbing something like a mapletree or tuba (possibly feliks) would be a more doable alternative