Using ⁶ for "^6" would be possible, but would take making a new class to process the operator, but that can be done.
For ° you could create an operator (right-associative) that multiplies its argument by pi/180, I suppose. If you want to make it work with NumberWithUnits, you would have to define a new unit ° that is equivalent to "degrees", but that could be done.
replace()calls that translate "π" to " pi " (with spaces so that it will not accidentally parse as part of some other word), and so on.
submitAction()function could be used to handle the replacements. It could use
document.querySelectorAll('input[type="text"]')to get all the input fields and loop through them to modify their values, replacing unicode characters by their equivalent ASCII representations. This would run when any submit button is pressed, before the form is sent to the server, so it should be possible to pre-process the unicode in this way.