Without debating the pros and cons of a low-carb diet here, I race
track very competitively without carbs, i log plenty of 4hr+ rides without carbs and i lift at a reasonable intensity without carbs and without experiencing any of the OPs problems. I do monitor my fluid intake, my sodium intake and i've been low carbing for a few months now including occasional intermittent fast but no carb-cycling or loading so i feel i'm quite well "fat-adapted".
based upon my N=1 experimentation, it seems to me that some people (ie, me) don't need carbs in the quantities that a typical western diet provides them to perform at a high level.
to the OPs question, as i said earlier, i reckon if you're low-carbing for a good reason and the diet's pros outweigh its cons then i suggest that your issues with the wobbles can be solved with a combination of electrolytes, water and time.
just on the topic of low-carbing, personally i've found that there's a far greater difference in power output on the bike between when i am or am not supplementing with beta-alanine than when i am or am not eating carbs. carbs are a bit of a non-issue, really...