This is the last mission that I have to complete, but I can't seem to come up with a good strategy to complete the mission. I always seem to inadvertently collect a coin or two along the way to 1750m. Is there some sort of winning strategy to complete this mission?
First of all, avoid using any vehicles, they get hard to steer pretty fast and you might pick coins by accident. So unless you are sure you can control your vehicle, either avoid picking them up or destroy them intentionally as soon as possible. In any event, turn off the magnetic vehicle add-ons if you have any.
Use powerups. Buy the Head Start powerup and when using it stay close to the ground. In my experience, 80% of the times you'll reach 750m without any coins. Grab a few Quick Revive powerups as well, use them only if you've reached a significant distance without picking any coins (say, 1250m). In the event you have a choice between death and picking up coins, die and revive yourself. I'd avoid using the Final Blast unless it's a last resort, you may end up collecting coins while you tumble away, in any case, don't use it if you have a Quick Revive unless you've used that first.
Picking up tokens is up to you, they don't count against you, and you might get a revive or a Final Blast in the slot machine, but if you use them and get coins or cash them in you'd lose your mission. I'd say - prefer to use powerups before spinning the wheel for the first time.
The mission isn't that hard, I've completed it successfully several times (I finished all missions 8 times by now), it's just takes a mixture of skill, luck and clever use of powerups.
What I've found to be very useful on that is to turn off ALL magnetic upgrades (vehicle and, avoid getting any vehicles on the way. while you're running, look to the right most part of the screen, the coins come in very specific patterns and are often easy to avoid if you remember the patterns. I have completed all missions 24 times and I am now on my 25th play through. the first 10 times, that mission was available on a normal basis (they repeated in the same order) since the big update it occurs less often, but still one of the hardest missions!
I have done all the missions 30 times each and have never had enough money to buy quick revives and small blast and soon. If you look at the right side or your screen and move away as soon as you see the coins, you should get it. Don't get any vehicles or spin tokens because they are harder to control and you might spin yourself $1000 which you do not need.