I have a 1.5 ton now and it can't keep my existing 750 sq ft cool when it's 95 outside. Roughly 400 sq ft of that is over an unconditioned garage.
I f I had a nickle for everytime I heard that one. Unconditioned garage will increase heat load. You should look into a whisper quite unit if noise is a concern. Two stage condenser to handle extra load requirment like lots of family or electronics, this does not sound like a builder grade application.
Far too easy to blame the equipment when little attention has been paid to the building envelope. It's not all about just keeping the air cool and dry. Your surroundings need to be cool as well, or you won't feel comfortable.
Other pro responders here have already advised you to not proceed without a load calculation. I add my voice to that. Anyone who comes to your home and just "eyeballs" a guess for what you need is wasting your time, and can become an expensive mistake if you go with someone like that. Same for someone who says "oh let's just add a return here and throw a few supply registers around, everything will be cool!" No, it probably will not.
Since you intend a home theater for the addition, you need to step up the quality of those you bring in to consult on this project. Big time.
Electricity makes refrigeration happen.
Refrigeration makes the HVAC psychrometric process happen.
HVAC pyschrometrics is what makes indoor human comfort happen...IF the ducts AND the building envelope cooperate.
A building is NOT beautiful unless it is also comfortable.
I had a company come out and recommend a Trane solution that was approx $3K more than the similar solution from American Standard. The guys I had out today use American Standard, they also mentioned that they typically use baffles and they need to do load calcs, etc. to really price it out. I liked their attention to detail much more than the guy yesterday.
The reason it won't keep up is probably because your duct work leaks and is pulling in hot attic air through the return and through leaks in the building envelope. It could also not be working properly as well (low refrigerant, low airflow etc.)