Going by the description of the clay soil base, I think a good size tracked excavator could do the job pretty fast. We had a pond dug in similar conditions by 100ish hp one and he moved alot of wet clay fill with no problems, but he's a pro of course.
A rough estimate is it costs $0.80-1.00 per cubic yard of dirt moved, and I'll guess it will take 6-8 cubic yards per yard of road length to make something an ATV can drive on, so a 1/4 mile isn't all that expensive.
Do a few holes by hand along the route just to confirm the clay base is always there and get a few quotes. Someone might have a dead spot in their bookings and be glad to have a week long job.
Sometimes $5k and done with it, is a good option! Our pond was quite a bit more than that but I'd never dream of getting a suitable machine for a year to do it myself.
