I was wondering about trying one of those kits sometime myself, Frost's do one which I've seen recommended too, though it comes to around £130 so I've been holding off. Worth it?
The tensioner should not need greasing - just a little oil ought to be fine. However, if yours is sticking then it is almost certainly suffering the very common problem that some grooves have been worn into it by the (slack) camchain and they are making it sticky. Get a tiny triangular file and clean up the edges of those grooves where the horseshoe meets the bracket, until it moves freely and smoothly. If not, you'll never get the chain to adjust! Hopefully it isn't worn too badly as the part is no longer available from Honda.
Oh, remember to fit the tensioner pushrod and springs before fitting the tension mechanism and joining the cases.