My last attempt yielded a hybrid double infusion single rest fly batch sparge. I'll detail that now.
Limited to my 4.5 gal brew pot (planning on a new / additional one) and my kitchen stove, heating huge quantities of anything is a little challenging. So get 2/3 capacity up to strike temp and add to (first time using) tun. Stir that while slowly adding grains. Lid on cooler, back to the faucet. Add a bunch more water to pot, heat to MASH TEMP - the grain in bucket is already at mash temp, heating water to strike at this point would cause problems. So that's the second infusion single rest. Alternatively use this as a perfect opportunity to do multi rest.
When that's about done start heating water up in a kitchen pot that I prefer to not use for beer although it is quickly being promoted. As long as it's below tannin extraction point I didn't pay too close attention. Begin draining tun into main pot. When it's full, "fly sparge" the contents of the kitchen pot into the (now) thick mash still in tun. Drain tun completely into kitchen pot. Add about 2L of water to the tun to maximize efficiency and boil volume - would have used more but ran out of vessels to hold it in.
This method though time consuming did yield the desired result. I hit my OG and life was much easier with the tun as compared to my previous BIAG attempts. It's also a hit in the wallet, before anyone can point that out. The relatively thin mash compared to previous attempts was a joy to work with. Small amount of sparge water never ran clear, I think perhaps next time my second infusion will be about half of what I used. Thin the mash out, guarantee no dough balls, but leave enough room in my kettle(s) for sparge water. Always learning.