Fining Lager

Hi all,
My first batch of lager homebrew (from a kit) has quite bad chill haze. I know I can leave it in the fridge for a few weeks to clear, but I was wondering for next time if it's acceptable to:

1) Rack off into a secondary after a week in the primary
2) Lager for a few weeks in the secondary
3) Add finings to knock out all the yeast and haze protiens
4) Rack off into a bottling bucket primed with sugar and some fresh yeast
5) Bottle and leave to carbonate as usual

If so then how much and what kind of yeast should I use at (4)? I have some saflager S-23, would that work if I let it foam up in a small glass of warm water for 15 minutes before adding it to the bottling bucket?

I not too sure if that process is the best option but it's what I do and it seems to work out fine for me. So far no real problems and I'm left with a crisp clean beer at the end of it. I Haven't gone for the addition of extra yeast as I sometimes end up with a partial mix in of existing yeast during my final rack from secondary but the saflager sounds like a good choice.