Make an IAP in a Restricted Profile
You could try temporarily unrestricting the account. Your phone must be rooted. I haven't tried doing this and have no idea whether or not it'll work. It's just idle speculation.


Make a full backup of the entire device, including all priceless user data such as documents, photos, and home videos. Store the backup on your home computer, or on a MicroSD card kept in a safe place.
Root the device. This carries risks, which I shall not list here.
Install SuperSU.
Temporarily convert the restricted profile into a non-restricted profile. Right now, I'm too tired to prepare a full set of instructions on how to do this. Instead, for now, you can pay a technician to look at this post. Upon seeing the post, she'll be able to figure out what to do.
Try to make your in-app purchase.
Set the profile to be restricted again.


I wonder if the in-app purchase would work, though. Would the temporarily-unrestricted profile have a Google account associated with it? If not, could it still make in-app purchases?

Maybe you'd have to add a Google account to the temporarily-unrestricted profile then remove it from that profile after making your in-app purchase?

Please leave me some comments about whether or not this worked for you.