I have to concur, Silver Seal does work, and it leaves almost trace of left over residue. Like ANY 'sealing agent' how well it works depends on an almost endless list of variables, which is to say, sometimes it works well and sometimes it doesn't. Certainly worth a try.
'Bars Leaks' is another great product, but I don't care for the color and residue it leaves hanging around in the cooling system, looks like 'rust' and 'milky water'. But it DOES work.
I don't think I would try to tighten the freeze plugs (core plugs or whatever you want to call them), I WOULD try some sealing agents first!
By the way, you should have an 'over flow' catch can of some kind. A hot motor when shut down builds up pressure and 'pushes' water out the overflow onto the ground (if you don't 'catch' it). The overflow container should have some water in it all ready, enough to cover the end of the hose. Hot water flows in, motor cools down, sucks the water back into the engine. Without a catch can you generally have to add water on occasion. I'm presently using an empty plastic Gatorade bottle, but my friend suggested a "Jim Beam" bottle might look better.