Revving while moving is only a limited few things:
1) Spun hub on your prop. - Scratch a mark across the inside of the hub that goes from the aluminum of the inner prop across to the nut that retains the assembly, Take it out for a spin and get it to rev again. Once out of the water, check to make sure the marks line up. A spun hub will usually only let you move forward just at or above idle before letting go. If the hub is spun, you'll need to send the prop out to have it re-hubbed.
2) Shift dogs are wearing out - The lower unit uses very coarse cogs that align when you shift. You need to do a sure and quick shift to clunk the dogs in place without grinding them. If you are hesitant and hear a rattle when you shift, you are shifting too slow. A quick way to see if the dogs are skipping is to hold the shifter with a bit of pressure while running the engine speed up. If it doesn't rev while doing this, your shift dogs will likely need to be replaced. This is not a simple DIY job, and you may need to find a shop with tools to do it.
3) Splines on the drive shaft have sheared - not a very common problem. When you drop the lower unit, inspect the splines for damage. If damaged, replace the driveshaft (you'll need to do this anyway to convert to short shaft)
4) Poor adjustment for shift linkage - Make sure that your shifter is securely engaging with a good feel to it. usually much more of a problem with remote shift/throttle. There really isn't any adjustment for linkage on a tiller.
One concerning statement that you made is that you've run this thing on the water for 10 minutes, yet you haven't dropped the lower unit yet?? These motors are EXTREMELY reliant on a proper cooling system, and the impeller in the lower unit is the most critical part. You should always inspect/replace this on a newly purchased motor, as you have no idea of the history of part. It is too critical to the functionality of the motor. I hope that you are seeing good flow of water out of the rear exhaust ports, I don't think the '75's had any tell tale yet.
My fear is that after running for 10 min, that you could have cooked the motor if the impeller was old or damaged. That could explain why it isn't starting after running for a while. If you have a compression tester, run a check on your cylinders. You want to be over 100 psi, although it will run with 80. You want both cylinders to be within 10% of each other.
If compression is ok, then it's time to start looking at the spark. But we can approach that after clearing the compression.
Good luck!