[PaulHoule]

(1) If you can recycle the old "semi-complicated algorithms" in some way you should. For instance if these are written in FORTRAN or C it is not that hard to write wrapper code to access them in a more complex language on the back end, it also may be able to compile them to webassembly.

(2) If you can't do that, or even if you can, you should build a test suite that works on both the old and the new code so your reimplementation is correct. This will save you so much suffering.

(3) If you want to make an app that has the same sensibility as a desktop app in 2020 I would look to React, Vue, Svelte or something like that.