Let me propose another approach that throws in the human element. How experienced in the machine operator? My suggestion uses the GIS after the fact as feedback to the operator. So this method relies on the human brain factoring in dozens of factors to decide the route. if you are clearing stumps, likely the trees grew naturally and probably grew in clumps or groves. A planted forest would have regular rows of stumps which is easy, you just follow the rows taking out stumps in one row or if the machine has sufficient reach, take out 3 or 4 rows at a time on the same pass. If the stumps occur in clumps, the operator can decide on the best route mentally factoring in least travel distance to the next clump of trees. Likely the operator will look ahead 3-4 clumps and optimize a short term route and a longer, more generalized route for the day. Other factors the operator will consider in their choice of route is where is their fuel supply to swing by before the tank runs dry, the terrain and obstacles if those are issues, a route that minimizes retracing steps, and where they want to start and end at the end of the day (presumably near their vehicle to go home).
Where the GIS comes in is if you track the machine's path with a GPS during the day, next morning you can provide the operator with a map showing his/her route the previous day. If the operator is open minded, they may learn and adapt and get more efficient by reducing back tracking and wasted movement. So more along the lines of time and motion studies.
If you are the machine operator, then I think is a great problem to solve! And if it was my paddock and my machine, I would pursue the problem just for the challenge.
The other thought is there may not be just one solution for shortest route. This sounds like an optimization problem. You would need to do a Monte Carlo simulation to try a large number of routes because each choice you make on which clump to go to next affects the next best route for many future segments.
Further, if this was my paddock and my machine, I would try each day to best my ratio of stumps removed per lineal travel distance or litres of fuel consumed.