I have been to Costa Rica 12 or 14 times (I'd have to look back in my journals). All have been trips for photography, or a mix of photography and research with students. I have brought just about every possible combination of equipment that includes 300mm f/4 w/ 1.4x converters on film bodies, 300mm f/2.8 w/ 1.4 and 2x converters on FX digital & DX digital bodies, 200-400VR on FX/DX, 200-500 on FX/DX, and 500mm lenses w or w/out converters on FX/DX bodies.
You will have the capacity to make compelling images with just about any combination of high quality telephoto lens and digital camera body. In Costa Rica, subject isolation & subject to camera distance is everything. If your subject is visibly isolated from foreground and background elements, a modest amount of cropping will not negatively impact your final photos. Of all my camera / lens combinations, I preferred the 200-400 f/4 on a D500 to anything else. Sure the 500mm lens allowed for a narrower field of view, but the 200-400 allowed for flexible composition and f/4 isolation. I, however, lean more towards mammal photography than birds. Were I a bird specialist, the 500mm (and beyond) would be my preference.
As for your selection of lenses, you should be able to buy an Ex or Ex+ 300mm f/2.8 VRI or VR2 for $2000 to $3000. There are currently one of each for sale on the FM buy sell board as well as from KEH and MPB. You can use the 2x converter in a pinch, but the images are not nearly as nice as when using a TC14iii. A D500 w/ TC14iii will yield and effective 630mm focal length. A 200-500VR will yield a 300-750mm field of view. If you are photographing birds on sets (common in workshops), then the 200-500 w/tripod is probably your best for flexible composition. You will be able to prefocus, and the AF speed will be quick enough. If, on the other hand, you are shooting more serendipitously (this is more in line w/ my photography), I suggest you go w either the 3002.8 w/ converters, 200-400 (no converters), or 500PF (no converters). All three of the latter lenses have fast AF motors and are weather sealed.
I'm linking my
Costa Rica portfolio (not updated from my recent pair of trips)... All of the wildlife was shot w/ either a 300mm f/2.8 (+/- converters) or 200-400mm lens.
One more thing... bring a wide angle zoom lens (24-70 or 24-120 or...), the landscape photography can be quite stunning.
regards,
bruce