I follow the logic of everything else you said. Could you explain what you mean by not working half and half, and why?
I mean that when you want to grow you want to work all food-tiles, when you don't want to grow you want to work all production-tiles.
Farms are pure food tiles(unless they are on hills or plains) and mines are pure production tiles.
Let's give an example, you have a city at population 10, your goal is to get it to population 20 and build an aqueduct, a forge a market a library, a caravansary and a university.
The most efficient way to do this is to start your city on full production, working no food-tiles at all (except the ones you need to keep the city from starving), at this point you're making 0 excess food and a lot of excess hammers. You start working on the forge and then the aqueduct, when the aqueduct finishes, you switch all the hammer-tiles over to food-tiles grow the city as fast as possible to 20 pop, when you reach 20 pop, you once again switch all your food-tiles to pure hammer-tiles and finish the buildings you need as quickly as possible.
This is the absolute fastest way to meet your goal, the forge adds hammers to the mines you're working and an engineer, which speeds up the aqueduct slightly, the aqueduct makes sure your full food-focus is as efficient as possible. Being at 20 pop instead of 10 when building the market, the library, the caravansary and the university makes sure you have higher production available, as you can work more mines.
If you were using lumbermills instead you would have no ability to focus your yield-gain, which is why farms and mines are usually superior to lumbermills.
I can see you might mean farm hills where possible, but don't understand the "all mines" at all.
Farmed hills are pretty bad tiles when it comes to yields, you mostly farm hills to help with adjacency bonuses.
How does the international one provide as much food? If you use it to get friendship with a maritime CS, you get +3.5 food in the capital, as opposed to +6 for an Internal TR, and commonly that quest will not keep you as a friend for long with that CS. Now of course if the trade route quest is particularly good than of course go for it, but I don't see that working out in general....at least in terms of food.
I was talking about he traderoute quests, they usually provide quite a bit of food and you get the food instantly instead of over time (of course that means it doesn't get multiplied by growth, but whatever). That being said if the quest is bad, there is no reason to go for it, but they usually land you like 30 influence and maybe 80 food, which combined with the gold and possible science is definitely better than an internal trade-route (at least imo).