That’s correct. The Tzitz Eliezer says that it is forbidden to undergo the surgery, but once it is done, the person is now considered to be whatever gender they transitioned to.
Yes, it is a tremendous nisayon for a frum person. I’m not sure about “ways to address that” other than talk therapy, a supportive Rav, supportive parents, and a heck of a lot of self-control and determination. Those of us who do not have this nisayon will never be able to fully understand how difficult it is.
The nisayon is not an “excuse” to have the surgery. It doesn’t make the surgery justifiable halachically. But likewise, outright hostility and lack of compassion from frum people to the plight of transgender people is not justifiable, either.