During my currently fruitless job search I've kept my PO in the loop about jobs/locations that could prove fruitful. He and his supervisor have both communicated to me that getting courtesy supervision and then a transfer should not be an issue in my case. They both said that already having a job in the receiving district goes a long way to getting a transfer, since you'll be stable there.
OP is on state probation though, so his situation is different. I would advise him to speak with his probation officer about what his options are in terms of "courtesy supervision". I looked up what the Interstate Commission for Adult Offender Supervision says about sex offender transfers [0] and it seems that sex offenders have it worse than other offenders. While non-sex offender transfers are on a "shall issue" basis provided some easily fulfilled prerequisites [1] the sex-offenders are subject to a review period of a maximum of 5 days after which time the receiving state may accept/reject their transfer.
OP, talk to your probation officer about what your options are. A move out-of-state may not be out of the question.
[0] https://www.interstatecompact.org/step-by-step/chapter/3/rul...
[1] https://www.interstatecompact.org/step-by-step/chapter/3/rul...