I have both Hugo 2 and SP1000Cu. At home I use Hugo 2 most of the time, which clearly beats my TA-ZH1ES and HDV820. On the road, I use SP1000Cu or X7mk2 with RE2000.
Now, interesting comparison is between SP1000Cu and X7mk2. For pure audiophile aspects, SP1000Cu clearly wins in all departments, but not with a huge margin. Actually, the difference is not so big.
But overall, I prefer X7mk2 because of the amp (I use AM5 module instead of the stock AM3A). I tested using various HPs (please see my profile for the details) and preferred X7mk2 80% of the time to SP1000Cu.
And I believe it's because of the amp section. AM5 is very powerful (not to the level of Hugo 2, though) and can drive large cans nicely, like HE1kv2. Even with RE2000, I enjoy most of my music better with X7mk2 than SP1000Cu. Considering the price difference, I think X7mk2 does an excellent job for the price (1/5 of SP1000Cu).
Now, to your questions:
SP1000
1) Are you sure that the LR balance problem is because of the SP1000 not the HPs/IEMs (including cables)?
2) EQ is not a strong suit for AK DAPs. I don't think it will improve even with firmware updates.
Hugo 2
1) Yes. Hugo 2 has enough driving power with authority for HD800S and HE1kv2.
2) With HDV820, when I use analog input, Hugo 2 has better SQ to my ears.
Hope this helps. YMMV.