Well, some of those goals are pretty well met by the AR-180, though I have not counted parts. It uses a medium stroke piston, a copy of the Walther G.43 system. The M1 carbine also sounds well in line with your ideas. Also, examine the M1 rifle (Garand) if you can for how a design genius makes parts perform more than one function. The old Mauser 98 is also the product of genius; one example is the undercut extractor.
As to your ideas, I am not sure what advantage a trigger cable and DAO would have over a conventional trigger. I will note that unless considerable thought is given to safety interlocks, a straight drive striker is at least as likely, if not more so, to go full auto than a hammer-firing pin system. And safety interlocks (like those of the Glock) are usually small and use small springs (violating your part limit, plus your "nothing under 3/4 inch").
I am not sure what you mean by "a single main spring for both recoil absorption and lug lock". In firearms terminology, the main spring is the spring that fires the gun (the hammer or striker spring). If you mean the recoil spring/return spring, I don't know of any gun that does not use the same spring(s) for both purposes, although I know of a couple that don't have any recoil springs, depending bolt mass to contain pressure sufficiently (.22 LR) and requiring manual bolt closure.
I also know of no gun that depends on a spring for locking the lugs. The spring may propel the bolt forward, but the locking is done by a cam of some kind that is very positive, and made in such a way that the gun cannot fire until the bolt is positively locked (or at least forward in a blowback design). Depending on a spring for a critical safety function may cause problems if the spring weakens or breaks.
Jim