Local...where? (That may help people with appropriate local knowledge give more specific advice.)
While the pay may be worse, you may have better luck with public sector tech jobs (they will certainly consider the offense in hiring decisions, but they may be less likely to use it as an arbitrary complete disqualification.)
HR is NOT your friend. That is another conversation entirely.
If you cannot find someone to give you a break for a job, then I'm betting your best bet will be to remove the middleman, and go the self-employed route.
It is NOT easy, but it can be more lucrative and rewarding.
That said, OP did use the word shameful.
There's very few situations where indecent exposure should even warrant a felony, and barring any sexual/predatory motivation I can't really even begin to understand why it would.
You might have better luck with startups. They're usually run by people who aren't cowards, and they tend to be allergic to bullshit. Also consider remote work if geography is a poblem.