Plastic isn't a "no-go", plastic is preferable imho for higher temperature work, as the tank is insulated.
57mm is less to work with than the 55mm of a patterson reel. It sounds like you need to work on loading technique and clean your reels and make sure they are actually dry.. a drop of water will make the gelatin very adhesive against the reel.. as opposed to a completely saturated amount of water which will actually load onto the reel.
The depth into the track is about 2mm from what I can tell, so you should be able to load a film greater than 57mm width, edited: below to 3.5mm
a 61mm width film looks like it has 1mm of wiggle room to move, so that would put a depth of 3.5mm (I assume) into the track a film can sit. At 59.5, your film should be able to sit inside both tracks (fully sitting on one depth of 3.5mm, it has still 1mm into the other side), but could easily 'pop out' on one side than a regular film, if you load it carefully you should be fine, if you are paying attention to loading you should be able to feel what the film is doing.
At 57mm, there is 1.5mm into the tracks.. thats counting an exact fit for 61mm width without any kind of movement to allow for slight differences of films.. which obviously there should be... you're left with less than 1mm of depth into the track from a 59.5mm room on a 57mm opening reel.. in fact, if there is 1mm of wiggle room, your film will not fit on the reel, as when it fully inserts on one side, the other side will be free/out of the track.
Though it would be good to test load a 120 steel reel with the old film, since it has a center clip which might help.