Switch, switch, switch…Who gets the desired match-up?

[Nevadaref]

A long-time officiating friend of mine had an unusual situation occur in a game last night, so he called and asked my opinion. I now pass this along to the forum.

A1 is fouled and is awarded 1&1 FTs. B2 & B3 occupy the bottom lane spaces nearest the basket. Coach A instructs A2 to occupy the space next to B2 and A3 to take the one next to B3. Hearing this, Coach B tells his players to switch spots. Of course, the two players from Team A then follow those players across the lane.
Each team is striving to achieve the rebounding match-up which it desires. The question is how to settle this. Which team gets what it wants? Does one team have to occupy the lane spaces first and then allow the other to set up as desired? We obviously can’t permit endless switching across the lane.

I gave my friend my opinion on this, but am interested to hear the thoughts of others.

Note: MLB recently created a rule for when a switch-hitter faces an ambidextrous pitcher. This seems to be the basketball equivalent.