Will tripled 18' 2x10 beams carry a tractor over a stream?
I just ran some structural checks and everything passes if you use Douglas Fir #1 planks for the deck. Anything lower quality will not work structurally.

Beams are fine as is, just make sure they're bolted/screwed together well. Also, make sure that the wheels on either side are centered between the two beams. Don't drive it directly over a single beam. This way each beam is taking 1/4 of the weight. You do not have something that's "over engineered", it's close.

Regarding the soil, the further away you can get from the soil drop off the better. If you can get 20' long beams, do it. I also recommend placing a continuous 2x10 under the end of the beams to act as your foundation, otherwise you may rip up the soil there.