What cartridge you shooting?
I'm thinking a 16" 308 with the same ASE SL5 suppressor would be as close as you can get to a "practical" hunting setup on an AI.
Pictured is a 20” .308 however with the longer 16” AXMC forend. Do you have an AX or AT?
I have 4 barrels across two AI’s. 26” 6.5 creedmoor, 20” .308 for range work. Then a 18” 6.5CM & 16” .308 used for hunting.
I do have an SL5i and SL7i-BL (pictured). However both are heavy beasts if keeping down the weight & or length for hunting. Might want to consider a lighter weight suppressor for hunting…. However if you taking the same set up on the range for some abuse the SL5 is a great shout.