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With the exception of a few commercial-type filters, you can't clean most filter cartridges well enough to make the effort worthwhile. Though you could rinse off the coarser particles, the clogging of the filter is accomplished by the finer particles which become embedded into the filter medium and are essentially not removable.
I suggest changing the filter more often than you do if you notice a drop off in water pressure... the benchmark indicator for filter replacement.
Your problem is not uncommon with well systems, especially newly drilled ones. The process of drilling produces large amounts of sandy rock "grit"... the color of which depends on your local strata… e.g. the composition of the bedrock. The well diggers flushed out most of the grit in the well before it could be certified as a domestic water supply. Though the grit is most likely non-toxic (only testing can determine this for sure), large quantities of grit entering your pipes will clog faucet aerators, damage faucet shutoffs and wreck your dishwasher, washing machine and toilet inlet valves.
Because of the necessary imperfection of the aforementioned well-cleaning process, you will still get small amounts of this stuff coming through your pipes for years. This most noticeably occurs when the well is run dry by overuse. A fully depleted well has water entering it at higher-than-normal speeds from the depths of your well that are usually not dry, flushing grit into the well pipe from the surrounding bedrock. This agitated (and agitating) grit is pumped unfiltered into your water system to do its damage.
Whole house filters ARE the best solution to the grit problem and your installation of two should isolate your pipes from whatever evil your well pump may send them! Nevertheless you will still have grit appearing for quite a while since it has already settled into your pipes. Take heart... it will eventually disappear, never to be seen again. Except in your filters, that is, which should be changed no more than monthly and no less than annually based on your observation of how much grit they collect.
By the way, two filters may be a little much. With most well systems there is a noticeable drop-off in water volume and perceived pressure with the installation of just one filter, especially if one of the more dense filters is used. I suggest that you either (1) remove the filter element from one of the filter canisters or (2) install a large particulate filter in the first canister and a finer filter (or charcoal-type for taste and odor) in the second canister. This second choice will keep the water flowing better by having the finer second filter do less work and stay unclogged longer! With either solution you will probably notice more water pressure throughout your home with no loss of filtering quality!