My friends boat was having a hard time starting so we took the cover off the engine, he held the key and I smacked the solenoid with a rock and it started.
But it would always start once the engine was warmed up.
The grease inside solenoid would get old and sticky and the warmth of the engine would warm it up just enough to let the solenoid move.
So I'm thinking, you could try holding the key in start position and if it is just a sticky solenoid, the heat generated by the coils in it might be enough to warm it up a bit to get it going.
The current should still travel through the solenoid just not the starter if the solenoid is seized.
You're not going to drain the battery, just hopefully warmup the solenoid.
The coils in all the other solenoids on the car draw about 20 mA but the one on the starter is huge andmaydraw about an amp. (they don't give the current draw of the solenoid in the book)
It's easy to try and you don't have to crawl under your car.
If it works, you won't need a tow truck.
You mentioned you're on a hill.
What about a bump start.
I've done it in forward and reverse.
(it's not good for the pre-cat but you've got a header anyway right?)