First, if you can't afford the LCD-3s, the -2s are still excellent. Since I got the -3s my -2s have hardly left their box, so draw your own conclusions.
Comfort issues are weight and clamping force. Yes, the Audezes are far from light, but I don't find them oppressive. Nor too tight, though if you have a wide head or need to pull the cups all the way out that could be an issue.
Having had all the Schiit you mentioned, I can say that the two stacks are very different animals sonically. The Bifrost/Lyr will give a fast-paced but pleasantly tubey performance. Really nice with the -2s. The Mjolnir is a detail and transparency monster, and will tell you everything that's on the recording whether you want to know it or not. Notably more dynamic than the Lyr, faster all around and tighter bass. But no added warmth whatsoever. (That's what tubes are for.)
The Gungnir is a more open and detailed Bifrost, and more flexible (I use it with both my HP and speakers systems.) Once I heard the Gungnir, I sold my Bifrost. The -3s/Gung/Mj combo is a thrill ride, one I take almost every day. But not warm and fuzzy by any means. This is not in any way a criticism, just trying to give you the most accurate picture.
For economy and flexibility, the Lyr and -2s will do well. I would spend the extra for the Gungnir. You can of course put the Lyr atop the Gungnir but they obviously won't make a neat size-matched stack.