Your question is a question that is asked by many musicians over a range of instruments, but I think that the real question is a bit more broad than the one in the original post.
I believe the real question your looking for is: "How can I make something that is unfamiliar familiar?"
The answer to this is frequency.
The reason why you have a difficult time moving between alternate tunings is that, as you mentioned in your question, you only rotate between them about once a month. Such a distance of time between changing tunings does not create a frequency high enough for the information to pass into long-term memory storage. Up until this point, the majority of your understanding and facility with respect to scordatura is that of short-term memory.
So, it stands to reason that if you want to become more familiar with them, have to use them more often. I would say that you should alternate between the tunings during your practice sessions - that is solo practice sessions - not a rehearsal with the group (at first.) Increasing your frequency will make them much more familiar and therefore reflexive.
Also, I inferred from your question that you have several guitars - all tuned to a different tuning. I am sure this works for expediency, but I would recommend using one guitar and changing all of the tunings manually each time. This will not only improve your ear and your familiarity with your instrument, but it will also help to get you accustomed to thinking about the instrument in that new tuning.
In terms of practice techniques, you have to apply the same techniques you used to learn how to play guitar in the standard tuning. With each alternate tuning, I would suggest that you learn how to play all of your major, minor, and modal scales in the 12 keys. Memorize the new patterns, see how they differ or are similar to standard tuning patterns, make connections. Doing this will further help to familiarize you with the layout of the instrument.
Also, if you know the names of all of the notes on the fretboard and your scales, it is helpful to say the names of the notes out loud as you're playing through them. This helps to audiate the pitches your playing and provide your brain more context to work with.
Learning a different tuning is no different than a wind or string player learning a different scale, or a musician learning to read a different clef. It's just the process of taking something unfamiliar and making it familiar.
Bodybuilders have big muscles because they lift weights. Artists have keen eyes because they draw. Familiarity will come with time, but there is no substitute for putting in the work.
Hope that helps.