I bought a proprietary radiator/cooling system flush (from Supercheap Auto, I think it was a rebranded Nulon product), needing 2 bottles for the volume, with the intention of DIY. but then got a mechanic to do it. Another mechanic had confirmed it as ok to use such a product. Not sure about L135s, but L120s get a build up of crud affecting no. 6 cylinder. It was successful, resolved the overheating, (though I now know my gauge reads +20C). Multiple flushing as Steve advises is good. My mechanic did an extra flush when the alternator belt failed taking out the front hose during a WOT test run I found out about afterwards. Good luck with it, your instincts to do it are right on.
Island Gypsy 36 Europa "Doriana"