Oyster mushrooms are an excellent choice, they are very adaptable and can make most inoculation situations work. They are also a good option because although they are primarily saprophytic, they can also be a facultative parasite as well. Thus while they won't parasitize an actively living tree, if it is on the way out, then it will certainly will.
I would definitely girdle the main stem. While girdling a tree will not kill the entire tree right away, in fact, it can take up to years for that to happen, the girdled trunk and
canopy will die within a few days. Two weeks sounds like a good option for a waiting period,
enough to let most of the defensive systems completely die but not enough to have it completely dry out or become the substrate of wild fungi. That being said, girdling will not kill the
root system, you will almost certainly have numerous watersprouts and other shoots popping up that you will have to cut back. However, the tree will be severely weakened and if you continue cutting back its new shoots it will die.
I don't think it would be necessary to wrap the stump, but I would look into covering the inoculation holes with wax. The sunlight may be a problem but you could try shade cloth or another barrier to help reduce that. If the log wasn't 6 feet, I would say to try and let some of the watersprouts or other shoots pop up to give it some shade for a bit before cutting them, but it may be too tall for that.
If you want to use another species, you could try Lion's Mane or Black Poplar Mushroom. Both are choice edible mushrooms. The former is a weak facultative parasite, and the latter is known to be excellent for degrading stumps. They are both considered native to the Eastern US to my knowledge but I think Black Poplar is more commonly in the Southeast.
I also found this link on North Spore they may help, under "Stump Method":
https://northspore.com/pages/grow-mushrooms-on-logs-videos
I would also check out, "Growing Gourmet and
medicinal mushrooms" by
Paul Stamets. It's a very comprehensive guide to mushroom growing and well-regarded. There is a free pdf on the internet archive and the section on oyster mushrooms is on page 299. A long document but Control F helps a lot.
Hope this helps,
Eric S.