Yes, even on medieval profiles we've tended to use Strange as the LNAB for this family name (presuming this is the same family name found in other parts of England) which was a variant that already started appearing in the later middle ages.
I am not sure this is always the perfect compromise, but at least your proposal would match what has been going on so far.
We can put other variants in CLN.
Actually the most common spelling for some centuries seems to have been a one word version Lestraunge. The au want a typical way to spell French words, as in John of Gaunt (named after Ghent, where he was born, modern French Gand).