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...
>Because I'm still on probation, I can't move out of state
This may not be true. I'm on Federal probation, not state, so it may be different, but you can have your probation transferred to another state. The receiving state must agree to accept you, which may be an issue as a sex offender. Best of luck.