How long is the Mk-114? The only measurement I know for sure about it is its diameter (14.1").
I checked the Mk-41 wikipedia article and:
I don't know about the 209" tactical canister but the 303" strike version should be able to fit a PAC3 with with an attached Mk-114 booster or a booster based on it.
You once estimated the length of the Mk114 booster as
72 inches (6 feet), which looks about right to me, eyeballing it compared to the 9-ft length of the Mk 54 torpedo payload. (This also jibes with the fact that the 14-ft LRASM plus VLA booster fits in a Strike-length cell but is too long for a Tactical one). Mk 72 is about 5.5 feet, so not much shorter.
The wiki numbers are the physical depth of the launcher, but there is stuff under the canisters in each launcher (exhaust plenum, foundations, etc.). The actual canister length for Strike is 22 feet (264 inches) and for Tactical is 19 feet (228 inches). The max missile length inside that canister is about six inches less than that thanks to seals, hold downs, etc.
Now, MSE is 17 feet long on its own; there is clearly no room for 5-6 feet of booster under it. There is the Tomahawk booster, but it's not the right kind of thing for this -- its job is to get 1.3 tons of Tomahawk out of the tube, pointed away from the ship in roughly the right direction, and high enough for the turbine to start after the booster falls away.
If they wanted to add a booster to MSE for naval use, I'm sure they could design one, but it would be quite a redesign. And as stated, LM's goal is for the missile to be interchangeable off the assembly line for both applications.