Don't mean to kick you while your down. I figure honest feedback will be helpful.

Now that I've Googled your name and read the articles there's no way. You committed the same crime 4 years apart. The nature of your crime is relatively benign as far as sex offenses go. However, it's such a shocking departure from societal norms it makes me wonder what other inappropriate things you've done without getting caught. As a hiring manager, there's no way I would risk it.

This post was an excellent hail mary attempt and probably your best option for employment.

Your other realistic options are freelancing for people who won't do a background check or develop something you can sell.

Edit to add:

Again, not trying to be mean, but when your picture came up I said "Yep, that looks like a guy who'd expose himself to minors". Grow your hair out, ditch the goatee, find more mainstream outfit, and, most importantly, take the picture inside. In your photo you're squinting and furrowing your brow which makes you look a bit threatening.