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?
Tamron's 70-300mm is f/5.6 at the long end, not even f/4, much less f/2.8.
Are you saying the Panasonic FZ200 has a 300mm lens (or the 24-600mm lens claimed)? If so, why is 4.5-108 (mm) printed on the lens? Because 24-600mm would be a lie. The lens doesn't care about the sensor behind it, focal length is an intrinsic property of the lens. Period. If you want to equate that to the FoV of a FF lens, fine - but putting an iPhone 5 (8x crop factor) behind a 40mm f/2.8 'pancake' lens doesn't mean you magically have a 320mm f/2.8 supertele lens.
Bottom line, a 300mm f/2.8 lens optimized for a 1.6x sensor would be.....the same size as a 300mm f/2.8 lens for FF.
Now, if by 'optimized' you mean 'would give the same FoV as 300mm on FF' then a 200mm f/2.8 lens would do that (but 200/2.8 on APS-C it would give the DoF of 320mm f/4.5 on FF). Similarly, the 108mm f/2.8 lens on the Panasonic FZ200 gives you the FoV of 600mm on FF, and the DoF of about f/15.