i think that the 19 trees per year idea would work well, and i would suggest that your purchase your own chainsaw to do the work.
Working with chainsaws is dangerous but if you know what your doing and keep the saw well maintained, then there is a much smaller chance of getting hurt.

Pigs or goats would prolly kill the trees really quickly if you needed a reason to take the trees down.

There might also be a local equipment rental store where you could rent a stump grinder by the day or half-day in order to clear the stumps.