I’ve not heard the Burson gear and I’ve only heard the Lyr 3 at CanJam, so I can’t comment on them (I should mention that the Lyr 3 may not be ideal for sensitive IEMs, you might need an iFi IEMatch).
I heard the Jot 2 on a loaner tour on another forum. I liked it very much. It’s highly versatile. It drove my Audeze LCD2-Classic beautifully, and there seems to be a consensus that the Jot 2 pairs exceptionally well with planar headphones.
It also did a decent job with my HD 6XX and HD 800 SDR, so high-impedance dynamic headphones might work well with it. The Jot 2 is slightly warm, to my ears, and given that I paired it with a dark DAC (a Massdrop x Airist R-2RDAC), the warm HD 6XX was, you’ve guessed it, overly warm. That’s just a function of less than ideal component synergy, not an inherent flaw in the Jot 2. The wider point is that the Jot 2 could do a decent job with dynamic drivers, and if you’re in the market for something ZMF, I’d recommend looking through the reviews on various forums to get a sense of how people like the ZMF and Jot 2 pairings.
With IEMs, I was quite surprised at how good the Jot 2 was, in some situations. For a dynamic driver IEM out of the SE output - in this case, I tried the Dunu Zen - I found that the Jot 2 worked well. I had just enough travel on the volume pot for it to be useable, but you do have to be careful, obviously, turning up the volume. Also, there wasn’t any problem with channel matching at low volumes, at least as far as I could tell. The SE output was also acceptable with harder-to-drive balanced armature IEMs such as the Dunu SA6. The SE output didn’t work for sensitive BA IEMs, though, as with my Andromeda 2020; too much hiss and noise came through from the amp - note, though, that the Andromeda is unusually sensitive. Even so, Jason Stoddard has said that out of the Jot 2’s balanced output, the Andromeda is dead quiet.
The Schiit multibit DACs should be fine for you, I’d think. You should check with others with more knowledge to be sure.
You could start with the Jot 2 and the internal multibit DAC module and later upgrade by adding a Bifrost 2, if you want that extra improvement - bear in mind @pennstac’s important point about diminishing returns. Another option, as it would give you slightly different sound signatures - and hence a bit more versatility - might be to get the Jot 2 with the AK4490 balanced DAC module now and then add the Bifrost 2 later on.
I’ll defer to others to describe the differences in sound between the 4490 and the MB modules, especially in relation to the Bifrost 2, but it’s worth keeping in mind that a DAC/amp combination that works with one pair of headphones may not fare as well with others of a different sound signature, e.g. my experience, described above, with the HD 6XX. I could imagine a scenario in which the BF2, Jot 2, and Aeolus combination might be quite (too?) warm. ZMF pad rolling would give you more options for tuning, but I’ll again defer to the ZMFsters’ expertise here.
TL;DR - Jot 2 could be an affordable solution for you; beware of component and headphone synergies. I hope this helps!