I'm looking for traditional/speed metal that's a lot like Rainbow. Bluesy guitars, great acoustical sections, operatic vocals, and the like. Rainbow covers, whether or not they sound like Rainbow, are also desirable.

All suggestions are much appreciated.

I'll have to give it a little more thought in order to come up with bands that write original material that sounds like Rainbow, but I can point you toward the Liege Lord and Heathen covers of "Kill the King." They're both great speed/thrash bands from the 80's in a style that "Kill the King" seemed to have long before that was even a genre.

Liege Lord
Heathen

dream theater do a cover of stargazer, IIRC

Mundanus Imperium did a tremendous cover of Stargazer (with Jorn Lande on vocals). Stunning cover.

http://www.youtube.com/watch?v=5bzRZ2WH79s

Tyr also did a cover of "Stargazer" which I thought was pretty good.

Riot - Altar of the King

If that song isn't heavily inspired by Rainbow I don't know what is. Amazing build up, great release, powerful fucking song. The whole album is killer but this is the only song that's Rainbow-esque I would say.

Astral Doors have a very Dio-like vocalist (in a good way, not a cheap clone) although they are more heavy/power metal oriented
http://www.youtube.com/watch?v=KeraUlvJDrA

Doing a song title search for "Rainbow cover" will reveal quite a few results. A particular favorite of mine is Sorcerer's cover of the ever popular Stargazer.

Speaking of Astral Doors, have you listened to their new album?

Have a look at Uriah Heep if you haven't already done so.