Smell that? It's sweet-and-sour scent of optical physics and lens design waking you from your dream...
A telephoto lens design places the 'virtual' aperture at or near the front element. So, a 300/2.8 lens is going to need at least a ~107mm diameter front element to fill that aperture with light. That front element is going to be big and heavy, and need a strong frame to support it. A smaller image circle would mean a slight reduction in some of the internal elements, but won't really make the lens smaller (or cheaper).
There's a reason we don't see EF-S telephoto lenses (except one zoom that actually starts in the normal range and has a variable aperture, meaning a different lens design) - there's just no real advantage to a smaller image circle at long focal lengths.
Well, I DO understand that 2.8 might be pushing it, but maybe a 4? Tamrons 70-300 is plastic built, for FF, and this would be a prime, needing less moving parts. (I think that kind of build would be at least OK)
Also, are you taking into account the size difference in sensors? 300/2.8 might be 107mm on FF, but it sure is not on the Panasonic FZ200. So, how big would it HAVE to be, if optimized for a 1.6x sensor?
Edit: Oh, I saw your answer.