I would use the hacksaw blade by hand, as well. Brass is soft - it's easy. Or a take a chisel and cut one of the ends off and then deform the other - you may be able to just pull it right out. If you're comfortable with the zip saw, though, sure that's fine.
Personally, I like using the two piece plastic tubes (something like what TH Marine has). If it lasts 10 or 15 years - great - it's an easy removal/re-install. The brass tubes don't last much longer. Maybe if they were made of bronze, they would last much longer. But thin wall brass won't (at least not in salt, anyways).
"Ideally", scrape away all of the old sealant on the inside of the hole by using a slightly bigger hole saw (a little hard to get started) or run a drill bit around the hole. The idea is that you can then completely saturate the hole with epoxy resin until the wood no longer absorbs any more. It's now fully waterproof. Use something like a baby bottle cleaner brush or cut a foam paint brush thinner. Just keep going and going for a while.
Oh... and yes, I agree... don't use 5200 (truthfully, even 4200 is overkill for this situation, but it's fine). 5200 has VERY few applications on a boat. Any decent sealant will work for this like LifeSeal. The internet loves to recommend 5200 because everyone just keeps regurgitating what they read - but VERY few, if any, of those people have ever tried to remove it. But that's the way it is - if it's written over and over on a forum, then it must be right... even though the recommendations are baseless.
"Sealant pushing out"... Don't put so much sealant inside the hole, to start to with. Just coat the inside with your finger.