It sounds as though there are several issues to be considered re. your query about finding the right amp for your Vérité or trying out different headphones. I don’t have a Vérité yet so these are just a couple of quick thoughts and suggestions - hopefully others with experience of these headphones might chime in with more specific advice.
Have you heard the Vérité out of a high-end system? I ask because you have a top-of-the-line pair of headphones but an entry-level DAC and amp driving them. This might be like having a Ferrari with a Fiat’s drivetrain.
Because I’m interested in getting the Vérité, I have been reading the forums and have seen people using the Echo with their Vérité. If memory serves, I think I’ve seen people report that Zach recommends it as an amp in its price range. I could be wrong, though.
In your case, it might be that the Echo provides a boost to the sound of your setup but that the DAC is holding back both the amp and the headphones. That raises the question of what would be a good DAC upgrade. The Bifrost 2 would be one option EDIT: but you should be mindful of the overall system synergy: the warm sound of headphones like the Vérité might, with a warm DAC like the Bifrost 2, and potentially, a warm amp, make for too much of a good thing; you might want to find an appropriate balance between warm amp/neutral DAC or neutral DAC/warm amp. This will depend on how the components all work together.
You might find it best to experiment with some used gear and to sell of those items that don’t work well together, at as little a loss as possible.
Torq speaks highly of the Hugo 2 with the Vérité, which would provide you with both a DAC and an amp:
Do you intend to keep the Vérité regardless, then, or do you intend to replace it with an LCD-X or HD 800 S? To help others give you better advice, it might help if you clarified some of these issues and provided a budget.
If you plan on having the Vérité and another pair of headphones, then your choice of amps might become more complicated, especially if you want one amp to do duty for two different headphones. It might also be worth noting that the HD 800 S and the Vérité are both commonly understood to benefit from tube amps. I can’t speak for the LCD-X.