I am gonna go against the grain here - while I like the cold/warm colours, I feel like most people are ignoring the fact that we have more team setups than simply 3v3 and 4v4.
I believe that merely following the colours in a clockwise direction gives the easiest, most intuitive and broadest solution.
Imagine a game with teams set up like 4v2v2 or 2v2v2v2 - or something entirely different. Who's pocket? Who starts where? What colour do I choose now? I understand that this might seem like a stupid example for some, but while it's a rare scenario, this may happen (there is more to this game than the competitive scene). Choosing your position in a casual game for the casual player would be ten times easier using this method, I think.
I made the image below for a scrapped project a while ago (ignore the last box) that shows how easy it is to choose the correct position, no matter what kind of team setup or player number you're going with.
View attachment 165043
The randomness is a different discussion. Some may prefer randomness between the flanks and pockets, while others may prefer to know who exactly you're playing against on the other team. I don't know which one I truly think is best here. The option to show/hide the colours in the lobby would probably be the best solution.
I like that you are thinking other settings than the standard ones as well, however, I am not sure that for those it really matters. I think once there is a more or less standard established, it will be easy for players to understand and know where they will be placed - and in the beginning, we might need charts like this regardless