OK, the AU7 was stuck in the BH7 socket on the LA2 last night and I could hear no difference. I did the swap about ten times. I wish I had an A/B switch, as you lose a little focus waiting for the tubes to warm up, but still, I heard no major difference. Both tubes run pretty cold in the LA2, as Dave says, they are not really being hit very hard in that circuit.
If anything, I noticed a bit more detail with the AU7. So, good to know. If you have a bucket load of AU7's and don't want to hassle buying the BH7, you should be OK for the LA2 at least. I did try using the LA2 for driving a Pultec (600 ohm input iron), and did not notice any ill effects.
One useful DIY project would be a 9 pin plug that you plug into the tube socket. Then, you would have two 9 pin sockets mounted on a board with a switch for going between the two for comparisons. This would save the tube socket from wear and tear, and also eliminate warm up time. Leave the heaters on, just switch the B+ back and forth.
BTW: Interesting to note that the LA2 will still pass audio with the 12BH7 removed, reminding us that the last stage is indeed a buffer stage that does little in the way of amplification.