First, a few assumptions have to be made: 1) the acreage involved is just 3.3 ac. (?), total; 2) the property, based on your desire to leave the "palms", must be in a "coastal" area, and; 3) the pine, being ~35+ years of age, probably has some "good size" and height.

The volume removed would probably not be enough for a "production-type" logger. There would have to be some operators who use a small skidder (or horses) which means they most likely fell the trees using chainsaws. They may or may not be able to control where the trees fall, so you may have "to live" with some damage to the oaks and palms. They would probably be hauling on tandem-axle trucks (log length, not "treelength") so the mill would have to be fairly close (say within ~30 miles). Sadly, in this area, the mills won't pay a small logger as much for his logs as they would someone who hauls "treelength" (which means the landowner gets less).

If I haven't completely discouraged you, check with the County Forester or a consulting forester. They should be able to provide information on a mill location. They may even know of a logger who does this type of small cut. The sawmill may also be able to provide the name/s of a small logger. In this area (n. MS and w. TN) and for this type of small sale, the landowner typically receives just 40 to 50 percent of the delivered log price paid by the receiving mill.

Hope this is of some help.