Something that could thicken the oil might insulate the sound and make it less noticeable. I had a car that I inherited that had a bit of a tick that bothered me and I used a "no smoke" product that a friend had been using in his 275K+ V6 Lebaron engine . The no smoke product quieted up the engine nicely. Rather than resort to that you could try the heaviest grade of oil in your car at your next oil change and see if that does the trick.

Im not a big believer in oil additives. If anything you could do more harm than good by blocking oil passages with a big blob of gunk that came loose in your "engine cleaning" process. If I intended on keeping the car I inherited (I sold it instead) I would have had the top end overhauled.

I have a friend who is a horologist (clock/watch repair). A clock in a way is very similar to an engine. While at a slower pace over the period of many years clock movements develop the same problems with "sludge and gunk" that car engines do. If you don't lubricate the movement frequently enough the oil that remains turns into a thick sludge. There are horologists that will fix this with a shot of WD40 and then clock oil. Eventually these movements are damaged even more by the cheap repair and require more work replacing parts during a major service. Since heads are somewhat "disposable" and are rebuilt this is not as big of an issue on cars. Having to remake parts on a 200 year old clock is a much bigger deal.

If you notice a trend in the cars I have in my list of vehicles they are all inline engines. This is mostly because I keep my cars for a very long time and plan ahead for engine overhauls. On an inline 6 or inline 5 one head is cheaper than two on one of the V8's. If your planning on keeping your car around for a while I would look into eventually having your heads rebuilt. Heavier oil, patience and a loud radio might buy you some more time though.