I already tested the greenaddress and I haven't experienced any issue yet with iPhone 6 I don't have experience on both edge and BRD. So only greenaddress that I could suggest to you.

All of them only have sweep option to redeem bitcoin from your old address they don't have the option to import the private key that you can use at the same time for both core and mobile wallet.

If you want to use your bitcoin wallet from bitcoin core to mobile I think you need to switch to android because there are more wallet option that you can use where you can import your wallet without sweeping.