I don't think you'd need to do anything very different in grafting persimmons than you would with pecans. It seems persimmons are most often grafted with one or another variation of bark graft. I've successfully banana grafted at least one persimmon, although I think the size wasn't there for a banana graft to really make sense. If you'd be interested in a thorough tutorial specifically about grafting persimmons do a search for "quality whitetail deer persimmon grafting". (Deer hunters like persimmon trees for deer bait.)

I might be careful about collecting scions from an unknown variety in Los Angeles to grow in Oklahoma, though. Hardiness isn't something I'd take for granted even in a solid zone 7, especially not in an area with irregular temperature swings.

If you can successfully graft pecan, persimmon will be a walk in the park. Simple bark graft works fine - and is what I do - but I've also done just simple whip grafts with 100% success.
Aftercare is the most critical part of the deal - persimmon is adamant about pushing growth below the graft, and it's imperative to check - almost daily - and rub off any rootstock shoots as soon as they appear.
They do need some heat to callus in, so I do all my persimmon grafts after the rootstock is pushing vigorous growth, and the bark is slipping well. Not sure about when to harvest scionwood in CA - I cut mine in Feb/early March here in KY.
cuznfloyd makes a good point about hardiness - some of the Asian persimmons that work well in CA may not be sufficiently winter-hardy, but...nothing ventured, nothing gained. Astringent types appear to be generally more cold-hardy than the non-astringents.