Can you fly 2000 miles on an engine that costs less than $500k? If so, what type of engine?
Your best bet would be an airplane/drone that is built from carbon composite and graphlite rod (pull-truded carbon rod with incredible strength - widely used in sailplane spars) powered by a couple of aviation diesels like the Austro Engine E4.  

The Specific Fuel Consumption of the E4 is .336 lbs/hp/hr.  Except for similar competing diesels, nothing in any traditional aircraft engine configuration comes close except the old tubro-compound mechanical-monstrosity radials like the R3350 that could get into the high 3s (normal gas piston engines are around .45 lb/hp/hr and turboprops well above that, around .5-.6 lbs/hp/hr).

The E4 is 168 Hp so two would give you 336 HP for take off, and the engine burns 5 US Gal per side at 60% cruise, or 30 lbs per side, so to go 2000 nm, if you can get the thing to cruise at 150kt, you need 130 US Gal capacity plus a VFR reserve, say 140 gal total, or 840 lbs of fuel.

So design an airframe that can haul, say, a thousand pounds of payload with those two engines and 840 lbs of kerosene, and is clean enough to go 150kt, and there you have it.