Should I ask?

Since it is a tournament it would be in bad form to ask your opponent to resign, it would be bad etiquette to ask your opponent to resign in a casual game. Your energy would be better used in committing to play good chess every time you come to play.

Yeah, I figured asking would be rude/presumptuous, especially in a tournament... especially if it had been a situation where forcing a draw might be possible.

As for the conditional moves recommendations, I did that where I could (where I was forcing him to move and he only had one place to go to each time) but it gets a little difficult once he's got open options and there isn't really any one move that's better than others for him.

Were it a face-to-face or live game, I wouldn't have even brought it up... playing out to mate would have been fine, it was just the three days per move thing making it look like it could take forever if he chose to keep going.

Thanks again!

 It depends. If it's a Queen and king vs a king, he should surrender. If it's some piece like a knight he's down, he should not surrender. Either way, don't suggest the resignation. Just be reallllllllllllly sadistic and enjoy every moment of his agony. That's what I do.

I never ask an opponent to resign.  I will sometimes ask them if they feel there is anything to be gained by playing on.  If they feel there is some point, such as experience or they really don't know how this game should be finished, then they are certainly within their rights to play on.  The only players I don't agree with are non-beginners who want to be checkmated. 

good question, tell him to RESIGN

I like to enjoy my wins.  If I'm about to win or up by enough that losing would be very unlikely I'll say good game, there's nothing wrong with that.