Deck screws undetectable and boards are rotting

I agree with Ecnerwal entirely. But, absolutely screw the deck boards down & don't use nails, unless you like them popping up & ripping your foot or catching a shoe or high heel. Screwing the boards down is structural, for mostly just the boards...it spreads the stress instead of snapping a board from a fatboy standing between joists.

Definitely, use the tar-paper & bravo on doing it in the past...almost no-one around me does it & laughs at me when I do it or point out it's missing. Their decks last maaaybeee 15-years & mine last easily 30+.

Go with stainless steel screws! Square-Drive like the old screws is fine, but mostly Star-Head is all I find anymore. I think chamfering the bottoms will only trap more debris on top of the tar-papered joists, this will also cause water to travel to the meat area rather than just the edge. Simply hosing, brooming or putty knifing out the new gaps annually should be greatly successful.

There is also this type of saw that may work ok for this job:

This type has a lot more control than a larger reciprocating saw because the base rests on the surface of the decking board. These do have disadvantages in that when cutting thicker materials the blade can wander from straight down and create a cut that is not square with the surface. This can be controlled to a large degree by quality of the tool, blade selection and limiting the feed rate in the cut.

One advantage with this is that there would be no need to cut the larger diameter hole. Just two corner holes would be all that was needed.