I'm not positive what exact configuration of hull-deck joint you have, but I have an Allied Seawind ketch that I did the same job with maybe 8 years ago.
If I remember correctly, I used 5200 for the joint it self. I used a knife blade to get the 5200 into the joint as far as possible.
My hull/deck joint is through-bolted so I used 4200 to bed the bolts.
To bed the teak toe-rail back down, I believe I used 4200, as I wanted something just a little weaker, if I needed to take the toe-rail back off.
I've never had a leak there since.
I wouldn't worry about saving the bungs. You really can't get them out without ruining them. Take a small flat-head screw-driver and give the top of the bung a sharp whap, and that should split it.
You can easily buy replacement teak bungs at a marine-store. They usually come in a bag of many. Just tap the new ones in the hole. They come in different sizes, so make sure you get the correct size.
It's not really as intimadating of a job as it first seems.
Make sure you use LOTS of clamps during the job.
"...and a star to steer her by."