So if I follow you are saying that securing a sprung teak deck with epoxy and without permanent screws can work (using screws only temporarily in the laying process, then removing)...your description of dealing with core rot is very much appreciated, though hopefully won't be needed...
Yup, the teak decks on todays top-quality boats are all 'laminated' (epoxy, etc. glued) to the FRG underlayment. When building they use screws, between the strakes, to 'engage' the teak to the epoxy/FRG, and then remove the screws and then fill the 'holes' with epoxy .... no screws left in the deck that can loosen and 'saw' the FRG. The best way I know to FIND the loose screws is to use a micrometer dial indicator and then put a lot of pressure on the strakes while watching the dial to move .... and its usually the damn screws holding the 'butt ends' that are the 'loosest'. Also if the deck has been rebunged .... usually to save cost the builders typically used a screw with a slight 'shoulder' (a small zone of no threads near the head). When re-bunging, sanding etc. many times the shoulder is now down in the 'hole', few threads in contact with the FRG .... and this doesnt 'hold' very long. So, if you need to 'rebung', etc. be sure to look for and REPLACE these very common 'shouldered' wood screws with FULL thread screws.
Teak decks usually can be 'restored' (re-caulked, re-screwed, rebunged, sanded) several times. IMHO - the best method usually includes a 'teak sealer' to prevent dimensional changes due to drying out, etc. ... and a good teak sealer wont add any 'slipperyness' and preserves the useful life of the teak --- SEMCO, Teak Wonder, etc. etc. etc. At $40+ per board ft. you want your teak to be 'protected'.
BTW --- the absolute rule for re-caulking is that the teak HAS to be completely and totally DRIED out and totally have LOW moisture content .... or any caulk, etc. simply wont 'hold'. This is especially true in the 'butt ends' where moisture will wick several inches INTO the strake. Its that damn 'butt ends' that change dimensionally and force the damns screws out/loose.
There is NOTHING in the world that can compare with the TRACTION of a wet teak deck, even a 'sealed' teak deck, ,,,, except maybe coarse highway asphalt tar-mac.