>>> This seems very stupid as I would like to swap between them frequently.
Nothing "stupid" going on here if the user is "smart enough". I do this any time I want to. Basically, you have two BT receivers you want to send the output of Dot to, right?
First, have only ONE of the BT speakers on. Assuming the two speakers have already paired to the Dot, tell the Dot to "connect bluetooth" and it will connect to the one that is on; even if music is playing already on the Dot.
OK, so now you want to switch to the BT stereo? Tell the Dot to "disconnect bluetooth" to shut down the feed to the first speaker. Now, turn on the second BT receiver and tell Dot to "connect bluetooth" again, and it should, but if the first one started again, just turn off its power. and try second one again by giving command to Dot.