BIAB strike temps are a bit lower, BUT you are typically heating more water for a full volume mash, I can't see it really being any faster to strike temps, IME perhaps even longer.
I would suggest an overnight mash in a cooler starting just before retiring for the night, and sparging and boiling the following day. While lacto supposedly kicks in quick, I think you could stay ahead of any problems with only an 8 hour mash in a decent cooler.
Another option is to mash, collect runnings and heat to say 190 - 200 degrees to pasteurize the wort, then lid the kettle and come back to it the following day. Trying to chill the wort and reheat it seems like a waste of effort. Letting the wort freeze seems crazy to me, I can't imagine how long it would take to thaw a kettle full of frozen wort and bringing it to boil...that's a lot of energy!
I have also had pretty good luck doing "no chill" right in the kettle, after flame out and waiting for the wort to cool to hop stand temps, I lid the kettle and come back to it the following morning and pitch yeast.
The biggest time and work saver that I have found is setting up my brewery in the basement! Having everything in one dedicated area and not having to haul pots, fermenters, propane tanks, and ingredients outside and then back down the basement to ferment is heaven! If at all possible, try and come up with a way to brew indoors at dedicated spot.