How many paintings are we talking about here (for an exhibition, I am assuming more than one or two)?
I believe "officially" UA will not allow a non medical carry on to exceed 22in.
You may want to contact UA to buy an extra seat for your items if it is more than one or two.
Finally, Since this is for an exhibition (assuming they MUST be there, otherwise people will be staring at a blank wall

) I would NOT risk learning the day of departure they will not be accommodated on the plane as a carry on.