Oh wow thought it was in the Upgrade settings that you could exclude groups from purchasing but I see now it's only if they have paid subs already and not by group.
I wonder if this will work for you and you can turn off purchases for a group but the gift button will still show. It probably removes the entry not the button but not sure.
I'm not very familiar with that add-on but, based on a brief glance, it seems like it uses user upgrades under the hood (as does this add-on) so I think you'd be okay using both at the same time. I'm just guessing though and haven't actually tried.
You can tell I only briefly glanced as it because I didn't realise it did that and thought it was only applicable to guests.
Don't think it'd work if the user upgrades page for logged in users was also replaced. I think content gifting would be unaffected (i.e. gifting user upgrades on posts and other content types) FWIW.