I second Sebastian Koppehel's remark (As I also alluded in my deleted-edited answer-comment) that the text can be understood in two different - however close - ways. I also take it in the sense of possibility as: "They ate everything, we have nothing left to eat" (and my answer will follow that meaning). As we see in English, I believe also in Latin same wording can be interpreted in both ways - However I suppose some constructions can be preferred given the meaning.
- After trying to look for examples, I would prefer, if possible, to remove specific reference to music and leave it implied. Having etiamnunc restabit quod scribam (c.f., Seneca: Semper enim etiam sapienti restabit quod inveniat).
Also c.f. cum persuaseris istas fabulas esse nec quicquam defunctis superesse quod timeant, subit alius metus (SenPhil.Ep.82.16.12); A question if we can replace quicquam/nihil/aliquid with musica - grammatically is certainly possible, but I feel it would somewhat shift the meaning, because it would make the main part quod (or in this case with musica, quam) optional grammatically -- it is like a description for the music, and would render this as "music left that I'll write" instead of "[music] left to write" for whatever difference is there.
Otherwise, after that, I believe using "musica ad scribendum" - which was my first thought seeing the question (If my intuition worth noting) is a very good choice; In two translations of Numbers 33:14 ("... where there was no water for the people to drink."): Vulgate: "ubi aqua populo defuit ad bibendum"; Castellio:"ubi populus aquam ad bibendum non habeat". I think your suggested ut scribatur is pretty much equivalent to ad scribendum and also good, but for some reason I prefer the former.
With respect to the above mentioned, I'm not sure that the gerundive is a good fit for the meaning I suppose, as it really hints towards necessity or that the music worthy to be written.
The verb: there are several options for it: supersum, resto remaneo; maybe for my first suggestion it looks resto is better (only because I see examples for this constrictions that lack in others so far). But I think they are good as well.