However, in high mileage engines, or those that have been poorly maintained, it is possible that synthetic will clean out sludge/varnish and you might find out where the existing bad gaskets or seals are!

If you have over 300,000 miles on the engine, you are obviously doing something right. Were it mine, I'd probably change over. Since it is yours, my recommendation is to keep using what you are using (because I don't want you chasing me with a big stick if you get a leak)