When I did the butcher block counter top in our kitchen I left a piece of cloth in a tray of urethane varnish next to the counter. Every time I passed by I gave it a light coat. Every 4-6 coats I would give it a light sanding to even out any streaks. It must have 12-20 coats on it not counting what was sanded off but they are really thin. It turned out pretty nice.
Looks like you are headed in the same direction. It looks better with each picture.