I've found a trade route that gives about 10m profit per run. How many runs should I make per tick before I hit the rapidly-diminishing returns point?
If unopposed? One or two of those will probably be sufficient, in combination with the other types.
If opposed (even accidentally) then diminishing returns doesn't really apply in the same way and the equations get very complex very quickly. "As much as possible of everything" at that point, try to spend about the same amount of time on each, you'll know if you're overdoing it because the influence will move faster than you expected.
You might also have options to combine activities - a mission sends you to another system; pick up some vaguely profitable trade goods while you're there - even if it's only 1m profit for your entire hold, it's also basically free in terms of time (and you might gt a pirate interdiction on the way back you can pick up an extra bounty from too). For that sort of thing you don't need to worry about whether it's into diminishing returns or not as it's always going to help out a bit.