Getting a stuck mash, from experience, is dependent on a lot more than just mash thickness.
From years of brewing on my recirculating system with grain bills up to 30 lbs in a 1/2 barrel keg with a V screen false bottom and a 500 micron stainless steel filter over it, here's what I can tell you:
The crush of the grain can change based on moisture content of that harvest. How well you get rid of dough balls during mash in makes a large difference. The total pressure on the false bottom makes a large difference.
The first one you can address with malt conditioning, it helps a lot.
The second I solved with a 20 ft/lbs motor driving a custom made stir rake.
The third issue depends on the vacuum of your pump during recirc (obviously not as bad during sparge), and the surface area of your false bottom vs the total weight of your mash (water and grain together). If the pressure on the false bottom gets too high you will get stuck, be it which ever of those variables you are messing with. Your surface area of your false bottom is pretty fixed I bet, same with its filtration, so lets bypass those.
If you add too much water from the top you can actually cause a stuck mash/sparge because you've increased the pressure pushing down on the bottom of the grain bed too much. Too thick of a mash and the proteins all conglomerate into a hard cylinder and you get no flow as well. General rule of thumb is that you should have 1-2 inches of water above what the grains resting height would be (easy to measure at sparge, hard during mash). Too much vacuum from your pump and you can cause a stuck mash as well.
To address all this in my system I've found the standard 1.25 quart per lb to be a good thickness, I put a gate valve on the output of my pump to prevent it from pulling too much vacuum, I always condition my grain, always use rice hulls with large amounts of wheat and/or rye but dont put the rice hulls through the mill, stir WELL during grain in adding the grain to already existing water, not the other way around, and then I maintain a decent stir speed during the entire mash, and give the mash 10 minutes of no recirc or stir before sparge while sparging at a hotter temp (168 or so) (note I fly sparge). Also note I mill at .029
With that combination of changes to the system I have had neither a stuck sparge nor mash in over 3 years brewing once a month with everything from a 18lbs grain bill up to a 30 lbs grain bill.
When dealing with a stuck mash/sparge the best way I've seen to deal with it is with what is called an "under-let". This is when you push water up into the mash tun from the bottom to lift the grain bed. If your system is not designed to be capable of doing that I suggest you change it so it can, it makes a huge difference when trying to deal with a stuck mash/sparge.
Hope that helps.