I vote for laminate as well.
MDF is cheap, so the cost to redo your current work would be minimal, and the benefits of going with laminate
are worth it in my opinion. I spent approx $400 on four sheets of laminate for my full size upright CAB and I was extremely happy with the results. Laminate is easy to work with and requires only basic routing skills to apply. However, since you're building a cocktail, CAB you could easily get by with 2 sheets max. of laminate (or possibly only one). Veneer could also work. It would definitely look better than simulated wood laminate but would likely not provide as much protection against bumps, scratches and such (plus good quality oak veneer can be expensive).
I concur with VinceVega regarding t-molding. The 5/8 MDF I used for my cab was the perfect size for 3/4 t-molding once laminated (5/8MDF + 1/16 outside laminate + 1/16 inside laminate = 6/8 or 3/4) . However, as noted in the thickness calculation, I applied a thin laminate border to the inside panels of my CAB for aesthetics which is why I didn't experience any over-hang.
My two cents...
Good luck with your project.
Breaker.