If you are working in LaTeX, you can change the parameter for above-line text to move the neumes higher. Something like:

\grechangedim{abovelinestextraise}{0.3 cm}{scalable}


Where you adjust that middle number to something that suits your purpose. This can go anywhere in your TeX file before the place where you insert your gabc file.

If you are only working in the online editors, you have less control over such things. One thing you could do is to use the pitch height specifier within nabc: following the neumes you want to move, you put h plus a letter, with the later letters going higher up. The default is hf, so something like hh or hi should move those neumes that are running into the square notes up. However, this feature is meant to be used to show pitch-height differentiation in the neumes themselves (this is pretty common in, for instance, Laon), so I would only use that as a last resort and wouldn't put such a file onto Gregobase or the like.

Thank you!