The sticking point seems to be that what your psychiatrist is recommending has some compelling logic behind it, but at the same time it's understandable that the side effects are a big burden.
In principle, you could get a second opinion, but even if you found another psychiatrist willing to adjust your medication, the underlying risk of making adjustments would remain. Ultimately you have a right to put your foot down about what you're prescribed no matter who is prescribing it, but that could create more problems than it solves.
The only alternative to a medication change that I can imagine would be to make a change or get a treatment not prescribed by your psychiatrist, but that would also not interfere with your medication.
Some possibilities might be:
1 Lowering your stress level. I don't know if that would influence what you're experiencing, but possibly.
2 Dietary changes. Diet can certainly influence how you feel, but I don't know of any particular foods that would be recommended.
3 Acupuncture. You wouldn't need a psychiatrist to approve this, though if you got this treatment your acupuncturist should know what meds you're taking.
4 Chinese herbal medicine. You'd need your psychiatrist to sign off on this because of the possibility of drug interactions. I don't think the risk of interactions would be high, but he still might object.
5 Aerobic exercise, or something like yoga. Similar to 1&2, it could help but it's also not clear if it would address the specific symptoms that you have.