Looking at SMB3's possibility of finishing all levels with the frog suit.
6-5
seems impossible for now. You might be able to walljump up the passage while holding a shell, but it most likely requires Left+Right bug. Or maybe you can clip in the very first room for a level skip.
6-Fortress1
can be finished with Left+Right. Since you cannot go through 1 block tall passages as frog, I was thinking if you can clip in the first room and get ejected to the boss, but I've not been able to do so, with and without Left+Right. The GBA version of that level does not allow getting ejected to the boss (and has similar restrictions in other levels as well).
All other levels look to be possible without Left+Right. Since 6-Fortress1 is mandatory, it would be bad to make an exception for that level (if we go for no-Left+Right). Otherwise we could have done "max%,Frog%".
You can climb up walls 1 or 2 blocks at a time with Left+Right.
edit: Producks told me these levels are posing problems:
World 6 f-1 and f-2,world 7 fort-1 fort-2, world 8 8-1 and fort