Are they leather? If so, here is my completely unsolicited advice. I work with leather quite a bit ( albeit not in hockey gloves) and my two favorite products are the foaming leather new, and olive oil. As with everything I say on here, I don't guarantee it for hockey gear ( although I highly doubt it'll hurt anything if shaving cream didn't) but I'd find a time when you aren't wearing the gloves for 24 hours and put a dab (a little goes a long way) of olive oil on a sponge and put it on the inside of the glove palms. Then I'd clean the outside of the palms with Leather New. The Leather New does add a little bit of tackiness to leather ( goes away with use, but is noticeable for about the first 2 or 3 hours of use), so if that bothers you, I'd try to find a beeswax conditioner.
Like I said, I don't guarantee it on hockey gear, but I've been using these techniques for decades on my horse tack, riding boots, gloves, and shoes. The Leather New is pretty cheap, lasts forever, and is nice to have around if you have any unpolished shoes/ boots. I like it better than lanolin which, IME, has a tendency top work it's way back out of leather, especially as it changes temperature.