A preamp or EQ box with a sweepable midrange will be your friend. I am very happy with the Baggs Para DI. It has two sweepable notching/boosting bands, one for high bass (useful for woofs), and one for mids (useful for taming the hard tone).
I will sometimes boost the frequency band in question to look for the worst sound by sweeping. But cutting the mids all the way and sweeping the control up and down will also show the best range to trim. Here are three mandolins (thanks to Graham McDonald) comparing an F5, a bowlback, and a McDonald mandolin. It will give you some ideas where the main resonances are happening, and which might be exaggerated by a contact pickup and in need of taming via EQ.
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