OP, I really don't know what you should do now. I doubt that Bitcoinker can change Bitcoin address on your account, it's not possible to do that on script that they're using.
Faucetpay also aren't obligated to compensate your losses. Because it was your fault that you used not your own, but FaucetPay deposit address.
What is your purpose of using faucetpay?
If you want to use a wallet to receive faucet rewards from bitcoinker why not use non-custodial instead?
For me, it's better don't use faucetpay and use a wallet that you have full control of or at least a wallet that you can able to backup private keys or seeds.
I think you're not very familiar how faucets works. Faucets are paying very little amount of coins, something like 1-2 Satoshi. So, it's impossible to receive coins directly to your non-custodial wallet. People have no other choice than using microwallets to collect coins until they will reach treshold to withdraw funds.
Though, OP made mistake there by using not his own address, but FaucetPay deposit address to get funds from faucets.