Well I while back I went through the same routine, but chose a different process.
It's too easy to sand through, so I used stripper and a scraper to remove the varnish
from one of the smaller pieces. I found this to be quicker than sanding. I had some spots that still had oil
or dirt, so I used teak
cleaner to remove the spots. The cleanup worked and I reused the pieces
Some of the other pieces were too beat up so I had to replace them.
I never wanted to have to do this again so I started with one coat of penetrating epoxy
to seal the wood
, then finished with 6 coats of varnish
Its lasted for ten years now.