Not sure about tuning on the 300 but Dave Slate has been working on these things forever.He rebuild a Diana 66 Gis years ago for me and it is still going strong.https://www.airgunwerks.com/
Not a rifle one really can per-say "tune" ... but SERVICE Yes. These guns are a high precision 10 meter gun, steel ring piston in lieu of a convention seal, short stroke and a modest spring energy. In factory form / tune the recoil is balanced to action of the SLED mechanics that damp its motion.Jack up the spring energy you just unbalance the system and often get a harsher & less accurate shooting rifle. Power gains if done are give or take 50/75 fps over stock IIRC ... not worth it IMO.If gun shoots fine with @ 8 grain pellets in the 550-580 fps range your in the sweet spot and strongly suggest you just enjoy the rifle for what it is and go no further in attempting to juice it up.JMO tho ... Tune? There's nothing to tune. This rifle is already maxed out from the factory. What Scott says is absolutely correct. During the rebuild/service process, you can add a hot spring for more FPS. You can accessorize it to the max with an eye cup, anti glare tube, knee rest, palm rest, front sight inserts, eagle eye etc.
What I am looking for is to have the FWB 300 serviced as nothing has been done to it since purchase in 1984. Shoots fine so perhaps the best advice is to leave it as is?