I don't know the answer to your question of the wort sitting and cooling for 90 minutes, but I don't see that it would be problematic.
Have you tried mashing your full grain bill in half of the total water volume, then drain wort to another container, heat/add other half of water volume to kettle, let sit for 10-15 minutes, then drain/lift bag, and combine the two different worts? This is basically a batch sparge process utilizing the bag as a portable false bottom. This will also save you 60-75 minutes by doing a sparge instead of two separate 90 minutes mashes. In other words, conduct one 90 minute mash followed by a bag sparge, rather than two separate 90 minutes biab's.