Headspace is something that you deal with in cartridge firearms not muzzle loaders. It has to do with how brass cartridge cases fit to seal the chamber.
It does not matter in the mortar if you have airspace, you do not have a tight fitting projectile. The windage between bore and ball will reduce the pressure
People are not using chambers so they can use thinner material, on the contrary. They are using chambers because they don't need the greater capacity.
If you make a golf ball bore size mortar with no chamber you need a barrel that is 5.169 inches in diameter to meet recommend safety limits. Walls need to be the same thickens as the bore. 3 x 1.723.
The Maximum recommended safe load for a 2 inch bore is 2 oz per inch of bore. Switlik's chart for small cannon stops at 1.5 inches and 500 grains. If you extend the track of Switliks charts you will find it come out to just at 2 ozs. or 875 grains at 2 inches. Using the 2 ozs. per inch of bore rule the maximum safe recommend load for the 1.723 inch golf ball bore is 754 grains of Cannon grade powder. If you load 754 grains of Cannon grade in a golf mortar and fire it, you will never see the golf ball leave the bore and you will never see the golf ball again.
This might be fine for flat trajectory guns like cannons, but in mortars it's a waste of powder.
If you really think you need a mortar without a chamber, what I suggest you do is get yourself a 4 in x 4 in post. Drill a 1 3/4 inch hole in the end until the hole is deep enough to hold the max load of 754 grains of Cannon grade powder. Now drill the hole 3 1/2 in deeper. That is how deep your bore needs to be. Now add another 1.7 for safe back wall thickness at the back and cut the post off and this is the length of your barrel.
The largest bore you can use without a chamber with your 3.250 stock is 1.083. Maximum safe load for 1.083 is 210 grains of Cannon grade.
200 grains is a lot of powder in golf ball mortar and probably far more than you need and after one or two shot far more than you will probably shoot again. Read some of the post in the safe loads and cannon plans sticky at the top
In my golf ball mortar 94 grains of FG powder will send a golf ball just beyond 200 yards. Let me qualify that. The 200 yards was a measured 200 yards. The golf balls were found on the ground just beyond the 200 yard mark; 30 or 40 estimated yards beyond the measured 200 yards. When fired only occasionally could the ball be seen in flight.
To make the golf ball go 30 yards all I needed was 23 grs. FG. To go 100 yards I needed 40 grains.
I suggest you use a one inch chamber. The one inch chamber has a maximum load of 175 grains. Using a block of wood drill a hole deep enough to hold the max charge. Measure the depth of the hole and add 3.446 for the two diameter rule for the ball and you have you bore depth.
You can trust use here on the board when we say 175 grains of Cannon grade or for that matter FG is a lot of powder for a golf ball.