A lot said and good ones too.
Let me add few more lines.
Forget about form factor of body and how it behave. Do not even get into silly conversion talks. Most of your subject are small for the given distance except that rare need for portrait you mentioned (Really surprised me). So the practical difference between 5Diii and 7Dii would be:
- A tad smaller field on later.
- Rapid sequence continuous capture with 7Dii. A major difference: So chance of finding the shoot you wanted in more number of image captures, RAW or jpg. You will definitely see the benefit in spot and action images.
- Same (Almost) AFing despite what is a major subject of discussion in these days. Both are excellent among the best in industry.
Difference you will see on lens side:
Yes a 100-400 will give you very much needed versatility and mobility.
F stop is boarder line and can affect you in low light or fast moving subjects.
IQ is very good and deserve to be called L class but by no means has the ultimate image quality of either your current 500 or proposed 300mm, that both have Cutting Edge quality if that is what you are after or your business demand (To be above average Joe). You simply wont get it with 100-400 or for that matter almost any other lens.
Yes 300 F2.8 is heavy but should comes as total treat compare with what 500 gives you currently. Still don't bet on it for a full even half a day hand held shooting or a long hiking to subject in difficult train. 100-400 will shine here.
Moral of story: If you can deal with what you have and seem happy, continue with 500mm on 7Dii. With your needs, you will probably see a positive difference.
If Same IQ is a must but other factors are important to you, strongly consider 300. added F stop also will come as a total treat on all fields.
Adding a 1.4 TC is a must for its negligible price, and will keep you at same optical reach you have currently with no weakness to be felt in terms of reach.
No matter whether you switch the current lens or not, I believe you need to buy an additional lens, a 100-400 for when need, demands its use and I believe by no ways its going to collect dust in your bag or hand.
If you trade/sell & exchange, your current lens with a 300 and 100-400, you may go even or with only a bit of boost.
Which combination is best for you? Your are the only person that should answer that.