I understand that if I filter my beer I will have a clear, sediment-free flat beer which will not carbonate with bottle conditioning.
If I reintroduce a tiny amount of the sediment back into the bottles, will I get a carbonated brew with minimal cloudiness/sediment, or will it take so much re-growth of yeast to achieve carbonation that I will have the same clarity problem as before?
You'll get some sediment for sure. To just about completely prevent sediment you'd have to force carb your beer (kegging). Sort of a way to experience it is if you buy a commercial beer that is 'bottle conditioned', you'll notice a little but of trub on the bottom of the bottom.
However if you let the bottles condition, then leave them in the fridge for a week or so, the sediment should all settle out to a little cake on the bottom and be clear. The the challenge is pouring it out w/o disturbing the cake. The technique is called a shoulder pour where you 'trap' what little sediment is disturbed on on the edge of the bottle.
Or.. just keg and bottle from the the keg :)
You obviously understand that you’ll be stripping the yeast out of your beer with filtering. That will need to be replaced in order to bottle condition your beer. How much should you put back in is a guesstimate in my opinion. If you reintroduce the sediment to your beer, you are back where you started, clear beer now made temporarily cloudy with yeast and the conditioning process. It will settle at the bottom of the bottle and depending on how you pour, you may get clear beer or not if the yeast gets stirred back into the beer.
If you want to clear your beer with filtering, fine, force carb your clear beer and use a beer gun to fill your bottles with clear nicely carbed beer. Or let your beer clear with a fining agent, gelatin for example, rack your clear beer off to another vessel and prime with 5oz of corn sugar for 5 gallons of beer, bottle and wait for the magic. Either way bottle conditioned beer will always have a sediment issue to deal with.
