Randy, I doubt a spreader truck would come out for less than a 10 ton load unless another delivery is nearby. Co-op's usually loan/rent towable sreaders. 10 ton of ag lime could never hurt though---just back the truck up in a few places and let'er rip.
The last picture you posted looks like a good source for clay fines in large quantity in a run-off, as do the bare patches shown in other photos.
If you still have the jar test water out, has it completely cleared yet? If not, and you want it clearer faster, you could use some alum. Your PH is great! Check for alkalinity and if it's over 100, then the hydrated lime would not be absolutely needed. If several ton of AG lime were added first, I'm sure the alum would be safe on it's own. Try a few dozen grains of alum per gallon from the grocery store to see if it clears your test water completely.
