What would you recommend for the criss-cross pattern of wrinkles under my eyes?

Start by using a really good eye cream which will hydrate and strengthen the skin and help smooth the appearance of the wrinkles. Then maybe a type of radiofrequency microneedling, or a heat treatment like Tixel, that can be used close to the eyes to rejuvenate the skin, or an injectable treatment like PRP to regenerate the under-eye skin and smooth out the wrinkles. Find a great practitioner in your area, book a consultation and see what they can suggest that might help you.