Hi, I’m currently running membership through WooMemberships, and I want to make different forms available based on membership level, which doesn’t transfer into “User Role”. Is this possible?

From your documentation:
If you want to show different user profile based on user’s role, it is easy. Suppose, you have three forms: form_1, form_2 and form_3, now you want to show form_2 to all users who have editor role, form_3 to all users who have subscriber role and form_1 to all other users on your site. Then, write following shortcode:

[user-meta-profile form="form_1" diff="editor=form_2, subscriber=form_3"]

Format is: diff=”Role_Name=form_Name”