I didn't see where you live. What large city do you live near, so we know the summer design temps?
Energy-wise, what is the house like? That bedroom is over a garage, therefore it may need extra weatherization performed on its floor & other areas.(?)
I'm thinking that with a high $ zoned system it would be important to do a Home Energy Efficiency Audit & then a House Load-calc so you know what to do to bring the loads down for smaller system equipment.
I would think, you ought to be able to get it down to 12-Btuh per sf; 2700-sf * 12-Btuh/sf is 32,400-Btuh. That wouldn't call for a 4-Ton system; that would help on the duct system & allow for hopefully longer runtimes, which is much better for equipment, for your pocketbook, & for your comfort. Just a thought...
Here in SW WI, I use a tiny Half-Ton 6,000-Btuh window unit to cool my +675-sf 1937 farm home's first floor, that is only 8.8-Btuh per sf. I use a large floor type fan to circulate the air through the 3.5 rooms, it keeps the rooms no higher than 77-F & 55% RH even under extreme temp-conditions.