Without knowing more specifics on your Trooper (year, etc), I could only estimate your vehicle's GVWR.
3,000# sounded kinda' low for a beefy vehicle like a Trooper. In fact, I found the GVWR for an '01 standard Trooper to be 5,510#
{HERE}. What is limiting you right now, is NOT the capacity of your vehicle, but the capacity of your current hitch.
As you noted, you can upgrade to a weight distributing arrangement on your current hitch to gain another 1,000#. Alternatively, for about the same (or less) money, you could remove your current hitch (and sell it to recoup some $) and install a 5,000# rated hitch. A 2" square "receiver" type hitch is mandatory IMO. Not that you will be towing 5,000#, but there's the unwritten "rule" in towing to go with a decent margin of over-capacity. The reason is that if there is a sudden mal-event (a swerve, fish-tailing on a slippery road, or even a sudden impact stop) the forces on the hitch go up tremendously, and those forces could snap the ball or the hitch itself. The same goes for the tie-downs. The "working load" for a tie-down is for a smooth towing condition. If you suddenly stop, the momentum of your load can easily out-strip the capacity of your straps, and "pop!" /forums/images/graemlins/blush.gif your load becomes a missile. A 5G impact with a 2,000# load will put a 10,000# stress on the tie down. I found this "towing & tie-downs 101" to be very helpful
{HERE}
I think you can manage with a single axle (3,500# w/ 15" wheel) to meet your requirements. Just to be safe, I would make sure that the trailer has brakes (at least surge, but electric better), and that the straps and hardware are sufficiently over-capacity. You'll tow more confidently and more importantly you'll be safer.