Allan, I can't remember if it says anything about 'infinite' punishment..hmm..I always have trouble reconciling our experience of time with God being outside of time and seeing everything as the present. So I don't have much to say on 'finite actions/infinite punishment'. If an action lasted one minute (like..murdering someone for example) the punishment would not be one minute even in our legal system. So I guess it's 'as long as it takes'; even for ever ('tis hard to imagine).
Well anyway if there's punishment it's likely to be very painful because if being with God is our ultimate happiness, then separate from Him is ultimate misery. I'm thinking that maybe people would realize why they are suffering once it all begins...dunno (and the next part would be repentance). It would be good if no one suffered of course, but then bad things happen to people on earth too, and sometimes it brings them closer to God. Like you said "And secondly, we are told that God as Father punishes and disciplines those whom he loves, for their ultimate good"
God is loving, but I agree with CS Lewis (and everyone else who said the same) that 'love' includes wanting the person the improve for their own sake even if it's very difficult. It's not just about wanting to see the person happy and
that's it (sometimes people feel happy even when they are actually damaging themselves). Like Lewis said He's the Father in heaven not the Grandfather in heaven
So either people go to hell because they can't accept heaven and it's physically impossible, or they are thus brought back to God in the end. Or..both
But I think we'll all agree that God would not punish anyone for His amusement or some reason like that.
It's almost incredible to think that someday there would be judgement, afterlife, etc...