There is no such thing as a “specialist” to submit. “I would be willing to pay a fee to get my new site accepted” does not say “I’d pay somebody to fill out the form for me”. It’s talking about being accepted, and that means inappropriate payment, period.
“There must be some trick that I am missing”
Two things, build sites with quality, original content. I only looked at your blackjack site, and it has copied content so something like that won’t be accepted. Second, dmoz functions by volunteers. Right now there are hardly any gambling editors so hardly anything is done. If you don’t like that, do something about it.
It’s fine if a person doesn’t care, but if you do, what dmoz needs is 100 honest, good, sane gambling editors.
Btw, I’m not an editor. There are at least two members here who are though, although as Randy points out he doesn’t edit in gambling categories.