I have the Nikon D500 and the Nikon D780 cameras. I bought the Tamron 70-200mm lens, I love it.
I next bought the 2X Tele Converter, it works great with the 2.8 70-200 mm, treats it like a 5.6 lens. I shoot a lot of BIF and want not need, a longer lens, I have the Nikon 500mm 5.6 pf. I am considering the Tamron 150-600mm, My local camera store tells me the lens with the tele attached will be very soft at the edges 300mm and 1200mm.
What are your thoughts? Is F/ 12.6 too slow to focus on my camera's? Does anyone have this combo? What are your thoughts?

I shoot birds in flight for income. So my images have to be sharp. If you put a 150-600 on your D500, you will get a field of view of 300-900 mm. Your saying that is not enough reach?
I shoot with a FF camera and shoot with a 600 f4 and a 200-600 5.6/6.3. I do not use tele converters because they down grade MY images. A 1.4 would be the minimum I would except. A 2.0 is just not worth using in my opinion. Yes, your camera store was wise to caution you on using a 2.0. Focusing speed and sharpness suffer.
My suggestion is to learn more about the birds you want to shoot and practice hand holding and panning techniques.
The image below was taken of a Black-necked Stilt. They are very fast and you have to really practice to get them in flight because they have falcon like wings and can change direction quickly. If I was shooting with a 1200 mm lens it would be almost impossible to track that bird. And with a 1200 mm lens you would have to be shooting extremely fast to get the motion to stop.
If you want wing tips to be sharp, 1/4000 sec. is a must.
My advice, learn to use the Tamron WITHOUT any converter.
My other advice, you already have a much sharper lens in the 500 5.6 Nikon. My further advice, get a NIKON 1.4 for that lens. But, with the 500 you have a field of view of 750mm 5.6 lens. You should not need more than that to get great images. You really need to practice your getting close techniques.
And you can shoot the 500 5.6 wide open and still get great sharpness, at 5.6 your backgrounds would be more out of focus and your main image would stand out more.
Good luck and keep on shooting until the end.

I used the Tamron 150-600 mm with a Tamron 2X tele converter often to photograph squirrels in my back yard and found the results acceptable. However keep in mind my several statements that in my opinion the quest for sharpness is frequently overdone. I am neither questioning nor criticizing those who prefer it sharper than me. Just stating my view. For me a good photograph must be pleasing, tell a story, show something interesting or teach. I consider sharpness of secondary importance unless a photograph is very soft.
My view is different regarding macro and micro photographs, specially those used for/in scientific publications or ones illustrating details, small structures or organisms. These must be very sharp. My Nikon lenses do that and so do other brand macro lenses.

The close up insert was taken with the Tamron 150-600 mm with either a 1.4X or 2X tele converter (lost my notes about which one it is), 1/1250 sec, ISO2800 lens at 850 mm (1275 mm 35 mm equivalent). Post production with Photoshop: auto tone, contrast, color and sharpened once. Regardless of how sharp or soft it shows how the squirrel hold the almond while nibbling on it. This makes the photograph worthwhile in my view. But, then I am the person who has written several times that in my view too much is often made of of sharpness. The image on the right is the same lens at 270 mm no adapter. Same post production.