After some poking I managed to lock Jimi behind the "B B ICK" without a chance to get out of there.
Same thing here - if Jimi fallsunder the textbox - he will be trapped there forever. Well, at least this time it's dry and cozy life sentence.
Somehow I met 3D-guy here. 
But he's unsummonable here.
Here is the place for out-of-bounds walks. If I jump and press left - it's very easy to jump out of the box here (sorry, can't screenshot this) .
And here is the one fun place 1 screen left after entering this out-of-bounds.
After jumping over that screen Jimi can reach this place from the unexpected side.
Also, after finishing Quest 1 Jimy keeps his superpowers and can dash and double-jump in the real world. But he will lose his powers and summoner's orb after game reset, even if there was a save with the orb and superpowers. This happens even if the save was INSIDE THE QUEST, and this really softlocks the game.
And even worse - if I reset the game when catperson holds my QUEST - it will forget this, and it seems there is the one and only Q in whole game, so losing it softlocks the game too.