I've seen the casing go straight to the ceiling in houses where the ceiling was low like in finished basements and it doesn't look too bad really. And if you plan on replacing everything eventually it's not an expensive fix. You'd just need to either pop off that small price baseboard to trim it back to fit the casing or leave it and just use an oscillating tool to cut it

I don't know if I'm interpreting this wrong but couldn't you just put some 3 1/4 inch door casing right over the top of that 2x4? The only part of the 2x4 you'd see would be the small reveal you'd leave by the hinges.