Mine used to do that when I first got it 5 years ago they seem to start leaking from where the plastic end tanks are swaged onto the aluminium core, poured in two bottles of Barrs leaks, no smell or small coolant puddles since. (it would leave a small puddle when in winter storage), no the heater core hasn't been blocked by it.
If you are not wanting to do that the alternative is a 700 pound ($1500)radiator and the labour to change it (unless you are willing to do it yourself)
The header tanks can leak (if they are the original plastic ones) most have been changed for the fabricated aluminium ones by now though which don't.
You may want to go through the hoses making sure they are in good shape and the clamps are tight, some are hard to get at and may have not been fully tightened up by past mechanics.
You should also sign up on the AMOC forum (If you haven't already) there are a few knowledgable blokes on the Bloxham section who can give you advice . If you know Latin you will get on like a house on fire with the character that run's it.