Yes, what I mean is:
Engines like this are quite common and no doubt a local owner would help in return for a ride in the plane or two. You might have to buy the coal...
Try attending a local steam rally and asking around. Now is a good time of year because the ground is firm. It'll take a good day to roll a strip of the size you mention obviously depending on the surface but I imagine soft soil hence the mole problem. It's hard work for the engine because it's pushing a wave of soil uphill all the time, hence the need for coal. You might also have to supply beer.
The engine in the picture is typical and weighs 12 tons, which spread over a track of 7' is much more ground pressure than a farm roller can apply. Obviously I can't guarantee it'll defeat the moles, but it worked for my (much smaller) strip. What it will do is put a nice surface on the ground once you've equalised the 3-4" ruts by further rolling and the soil springing back naturally.
The ground must be dry though: a stuck steamroller is not something you can call the AA for!