I checked and it looks like Truck America Training (www.tatcdl.com) in Shepherdsville, KY is a good one.
The other decent one is in Sellersburg, IN which is a vocational & technical school (www.drivebigtrucks.com)
If you know which company you want to work for, call and ask which one they hire from. They're both 160 hrs. which is ideal.
The one in Sellersburg advertises :
NOW TRAINING IN AUTOMATICS COMPANY WIDE!
Some drivers want stick shift training, so they're probably letting them know ahead of time, they use automatics.
I don't think it matters much anymore because as you say, most companies are phasing out stick shifts in favor of automatics.
I read that SRT (Southern Refrigerated Transport) still lets drivers choose between autos and sticks, but is gradually doing away with their stick shifts.
You still plan to move to a state that borders California or moving to Missouri?
I recommend not having a restriction just because if you want it ever drive it say a local job or something and they only have a stick you best not have a restriction because they more likely ain't gonna let you test out in it. The automatics are nice some are better than others but it's always nice have the option be able use a stick. Mega carriers maybe all going autos eventually but constructions companies don't need the newest and greatest stuff same with oil field they just need it to work.