Does anyone have tips for filling the tunnels of the wraps around the guide foot without making a mess of the blank or the guide?

If you use a thin enough finish and don't coat the threads with CP, I've found that the finish will penetrate the wrap and actually work its way into, and fill, the tunnel. Also when you apply the finish start at the guide foot end and work your way toward the guide ring. This will eliminate any trapped air. My first coat is very thin and just covers the threads. After about an hour or so you will notice how the finish will start to exit the tunnel and completely surround the guide foot. I've never had to use a tooth pick or anything else like that to close the tunnel. LS Supreme works great.

Mike;
Do a search, there was a similar thread not long ago that covered the best tricks

i can tell you from experience that if you don't fill the tunnels on a spinning rod, you may have guides with play in them. search for loose spinning guides, or some variant of that.

bottom line, hold it in your hand, and place drops of finish at the tunnel witha toothpick. also you can use alcohol to wipe off any wet finish mess you have.

Capillary action. Start at the "toe" of the foot and keep placing drops on top of the thread as it's absorbed into the tunnel. Do not go near the opening of the tunnel until finish has started to come out on its own. This only works on CP-less wraps and only with freshly mixed (I use LS Supreme) epoxy. The thinner the epoxy, the quicker it flows in.