Did you include a small transaction fee in the payment? Otherwise it can take hours to confirm.
Is that correct ?
I thought the transaction fee (or lack of it) can affect the speed of inclusion in a block (& 1st confirmation), but there are 4 confirms already so doesn't that mean it is already in a block and only time needed for rest of confirmations (barring a major failure of the Bitcoin protocol) - or am I misunderstanding it ?
You are right. The fee only affects inclusion or not of the tx in a (first) block. All subsequent confirmations are just next blocks in the chains. So if your tx has got 4 confs already, you just need 2 more blocks on the chain and you'll get all 6 confs.