I'm not even going to ask why or how you drilled a hole in a cast iron radiator... I've used JB Weld to successfully and permanently fix cracks in radiators, both hot water and steam, but nothing quite so dramatic as a 3/8" diameter hole. Your best bet, I would think, would be a mechanical plug. Go to a heating supply store that handles goodies for radiator systems and see if they have tapered plugs used to cap holes in radiators that have been either moved or renovated or converted from steam to hot water or vice versa. My guess is that you're going to find something that will work. You'll have to ream a tapered hole to match the plug and then tap threads into it. All in all a pain in the butt, but a LOT easier than trying to braze it.

The answer to your question about "miracle chemicals" is "oh hell no!" How long ago were these installed? You need a good answer from your plumber/manufacturer and one that doesn't involve a dime out of your pocket. Look, you have a defective product/installation. If it's a year or less, they absolutely need to stand behind the entire cost of repair. More importantly, they need to assure you that the actual problem has been addressed - you don't want to be replacing all of these in 3 years.

I have central heat and would not recommend it over radiant heat using radiators. I would look at a company like Myson and I am sure there are others that sell more contemporary and smaller scale radiators to replace your bulky ones. Best of luck! Here is a link that might be useful: Myson radiators

My house is 1260 square feet on two floors, with another 630 square feet in the basement. There are four radiators for each floor, and a gas-fired boiler in the basement. The basement has no radiators, but I have three manifold ports open for future expansion. I ran Everhot oxygen barrier PEX, but left the iron pipe sections running down to the basement and put PEX adapters on the end of each down-pipe. From there I ran the PEX to a manifold like one of these https://www.pexuniverse.com/radiant-heat-manifolds.  The manifold has individual flow meters and a balancing valve for each line. IIRC you can also buy an electrically operated balancing valve that could be turned on and off to zone the system. I put the two manifolds near the boiler, which was in one corner of the house. That meant some fairly long PEX runs to get to the other corner of the house. I also had to dip the PEX runs down low enough to get under the steel beam in the basement, so they are a bit curvy in that area. However, it went in with no problems. I can go to the PEX manifolds in the basement and see the input and return water temps for each manifold. I can also see the flow rate of the water running to each radiator. One surprise for the balancing valves is that they do not completely close off the flow, so you can't use them to completely shut off water to a radiator. That would have been convenient if I have to do work on one radiator. I had to install caps on the unused ports to completely cut off the flow. FYI - I installed the manifolds (referenced in my link above) upside down because all my radiators were above the manifold and that made the routing easier. It all works fine that way, except the labels and temp gauges are upside down. Bruce