There is a vampire load on the 0-12v side of these trucks, so the 11.1v(25% charged?) there doesn’t surprise me. That leaves 12.7 on the 24v side which isn’t terrible(about 90% charged). 11.6Vrunning isn’t good on the 12v side but the total you gave indicates the 12-24 side is seeing 15.5V. This tells me your alt is probably OK, but the the 0-12v batts are either really discharged and overloading that side or you have a bad battery causing this.
Now run those same voltage checks at the large alternator output terminals. They should be the same there. If not, you may have a bad connection between alt and batts…
Same advice I gave Berzerker applies to all these trucks. Check and charge each battery individually, check all the connections at battery, polarity box and alt, check all grounds at battery, starter, alt and cab.
in the midst of milspec madness they specced a grossly oversized battery bank for the alternator they chose. They should have specced 2 batteries or the 200A alt should have been standard. They finally fixed this on the A1R.
like I recommend to everyone, you should drop to two batteries. It is more than enough power for the truck(bigger than Cat specs for these engines) and is a much better match for the alternator so will charge them better/faster. You can actually do this right now as your 12-24 batts measured 12.7v/90% charged, you could pull the two 0-12v batts(outside pair) and shift one of the 12-24 batts from it’s inside(close to frame) position to an outside position and re-attach the cables for that position. Tape over any unused battery connections.
With batteries at that state of charge in play, I would expect the alt to go right to it’s rated outputs(14.1/28.2) after startup…
Your alternator will thank you…
then you can work on the trans issue, which with good power applied may not really be a problem…