If you put yourself in the right seat/plane, you *might* be able to carry it on.
In a similar situation, I easily brought a large painting framed w/glass (24"x36"x2" I think?) on board AS SFO-JFK.
I strategically confirmed myself in window seat 2A (or 2F works the same) in F on a pre-retrofitted Airbus. There is an incredibly generous, wide space to securely slip a painting between the seat and the window in the second row of first class on those planes.
Whether someone will stop you before you get to the plane, is up for debate, but there is space for it. Not sure if 30" is too wide for the TSA X-ray belt or not.
Another potential space is the coat closet in F on the 737s. They are usually 40" tall, not sure if they're 30"+ deep though.
Best of luck!