I've been using StarSan to soak my corks before putting them into the Belgian bottles. I haven't tried one of the bottled brews yet, since they've not been in there long enough. I did let the corks sit in the StarSan while I was getting everything ready, then drained them when I racked the brew onto the priming solution. They were drying to the touch, but you could see some moisture when they were compressed during the corking process.
I would check the depth you're pushing the corks in (set it with the first couple) to make sure the cage goes on properly. I've been leaving as close to 1" head space under the cork as I can with these bottles. Which means the corks go in 3/4"-1" then the cage goes on top. Sometimes I need to hold the cage down as I wind the wire on it, but that's ok.
I would also highly recommend getting one of the wire winding tools for the cages. I didn't the first time I used them, going with a Philips screwdriver instead. A few bottles in, I was bleeding from the metal cap on the cages. Those suckers are SHARP! I would also hold the two vertical wires closest to the loop you wind, to make sure they stay straight. Put the bottom of the cage under the bottom lip of the top (not in the groove) and you'll be fine.
For adding yeast, I would only do that if you've had it in secondary for an extended period (over a month) and there's nothing on the bottom of the carboy. You can always grab a bit of the bottom yeast while you rack, to have some more in suspension to munch on the sugars you'll be adding. Unless your brew has hit the limit of the yeast's ABV tolerance, it will wake up when you introduce more sugar to it. I'm pretty sure that you'll even get carbonation if you don't grab any of the bottom yeast (again, unless it's been flocculating for an extended period of time).
I hit my old ale with some fresh yeast (packet of EC-1118) before racking it over to the bottling bucket. I had it in a corny keg for about 5-1/2 weeks (sitting on oak chips) and I did a really good job of not pulling any trub over from primary. I made sure the new yeast was still in solution when I racked over (the bottom of the corny was CLEAN) to the bottling bucket. The brew has been in bottles for just over a week now. I'm planning to chill one down after the 2 week mark to check on it. At 8.1% ABV, I don't see myself drinking more than one of those an evening...
I'm using the Belgian bottles for my bigger brews. More due to the coolness factor of having a cork to pop when you open them. Plus, I've been able to get them pretty cheap from the LHBS. Until I started buying the Belgian's, they had not sold any in over 5 years (since getting them in)... I'm slowly buying up their inventory. I think I've already purchased about half of what they had in stock...
I would do a dry run with one bottle to see how you need to set your corker for the correct depth. That's probably one of the more important steps. I don't think I'd use more yeast in the brew, unless you're over the original yeast's ABV tolerance level, and it's been sitting for more than two months. I bottled up a big brew (9.7% ABV) that carbonated just fine. Of course, the yeast I used was tolerant up to 12%... Basically no yeast was visibly transferred into the bottling bucket, but it still had enough in suspension to carbonate.