If you "want to go professional about it", then stay within the spec of the allotted space.
Maybe you can put two inductors in series or in parallel.
Another possibility is to mill a big hole in the PCB, and mount the inductor from the underside.
I do find it strange though to use PC104 in a high altitude balloon.
PC104 is big and heavy. Does not matter much for an industrial environment, but a high altitude balloon is a bit different.
Also, Inductors that can handle 100A
If you've been using this design for 40+ years, then maybe it's time for a complete revision. Maybe build something that is the size and weight of, for example an average phone?
Including batteries!