For close to 20 years I've used gimbals with several large lenses including 300mm and 500mm primes that do not change size, as well as with a 100-400mm that does. While internal focusing (IF) lenses and internal zooming (IZ) zoom lenses balance best on a gimbal because the equilibrium doesn't change, it certainly is possible to use a gimbal with a lens that changes size and equilibrium. I do it all the time.
A key factor is all the lenses I use on gimbals have tripod mounting collars. Even some use smaller, lighter lenses with collars I don't use on a gimbal because equilibrium is more dramatically upset AND because those lenses just don't benefit much from the gimbal. They just feel "uncomfortable" to use on it. In my case, lenses I never use on a gimbal for these reasons include 70-200mm f/2.8 and 300mm f/4... each of which the lens alone weigh more than the original poster's entire Sony RX10 camera with it's non-interchangeable lens. With all the add-ons being discussed (a gimbal, a long lens support and probably an L-bracket unless only horizontal/landscape shots are ever taken)... their camera will probably double in weight AND be slower to use.
Add to this that the original poster asks specifically about using a gimbal to shoot birds in flight.... which is usually not advisable. Although a gimbal is faster to use than some other types of tripod heads, it's slower than shooting hand held and the gimbal will make it more difficult to track smaller, faster, erratically moving subjects.
So I stand by my original response.... The OP's camera and the subject matter the OP wants to shoot with it simply won't work well with a gimbal. They need to look at other options. I don't know what those might be, but suggested... Perhaps a monopod with a monopod head (which differ from tripod heads in that a monopod head only has one axis of adjustment... tilt). "Shooting sticks" or a "belly pod" are possible variations on that idea.
Some more ideas:
Wimberley also is now offering a "MonoGimbal"... a gimbal head specifically for use on a monopod. That might be faster to use and may work for BIF photography. I have not tried the MonoGimbal and can't say. I think Steve Perry has a video about it on Youtube. Might want to watch that and see what he thinks about it. While it may work for BIF photography with a DSLR and a lens with a tripod collar, I don't think this is a solution for a Sony RX10. So I doubt it will help the OP. Not to mention that the MonoGimbal ain't cheap at $179 plus the cost of a sturdy monopod to use it upon and the necessary Arca-compatible plates for lenses to be used upon it.
https://tripodhead.com/products/monopodhead-main.cfmdsmeltz wrote:
Don't know if they still make them, but a gun stock mount is great for birding, especially for the big hawks during migration.
That's an interesting idea, too! I forgot about those, even though I used one briefly many, many years ago for sports photography with film cameras. I don't remember if it was made for photography or if I adapted something else. The main problem was it's bulk. A modern one made of plastic with a minimalist or "skeletal" design might be a lot smaller and lighter. You typically need a wired "remote switch" on one of those, to be able to fire the shutter. (I used a standard cable release... but those don't work with modern cameras.)
Bushhawk is no longer made and the BIF Bullseye appears to not have gotten "kick started". Maybe some of these others are available, or a Magpul AR-15 stock could be adapted:
https://www.google.com/search?q=camera+shoulder+stock&client=firefox-b-1-d&sxsrf=ALeKk00DloOvQqU8_kAowWlplh0LcTxhnw:1618418989042&source=lnms&tbm=isch&sa=X&ved=2ahUKEwiQ2MHHmP7vAhWkFzQIHX2jACYQ_AUoAnoECAEQBA&biw=1920&bih=1106I recall I also briefly tried out a "shoulder stock" that attached to a monopod. That was quite compact and lightweight. I don't think it was all that helpful for me and don't know if it would help the OP with their camera. Manfrotto currently makes their #361, I think. You'll need a monopod to use it upon, too.
Finally, another thing that OP might want to try one of the "pistol grip" type tripod heads. Those are pretty fast handling and might work for some BIF. Maybe on a tripod or a monopod? The main drawback is they aren't able to support very much weight, but that shouldn't be an issue with a 2.5 lb. Sony RX10.
https://www.bhphotovideo.com/c/products/Tripod-Heads/ci/140/N/4075788769?filters=fct_head-type_1544%3Apistol-grip-heads