Wow this is almost identical to my situation. I am using two small temple pieces at present and I'm reasonably happy with the outcome but I use walker non-shine tape and I've noticed that it seems to be easily peel-able by the a day or two. I make sure the head is dry and secure. I use 2 small partial pieces of about 2-3 inches in size.
It's not that the mini-wigs will come flying off in the wind as they are fairly secure but you can peel them off again after 2-3 days, I'm wondering if I have an oily/greasy head or I'm doing something wrong in my process.

All the best.