The Oil Drum

24 gpm, about 5 garden hoses on full, can give you real erosion problems unless it's really spread out. Tubing would require a maze to cover 4000SF.

Furrow irrigation is the choice among growers with flat land and plenty of water, which you appear to have. It's quite effective, having complete field saturation, as opposed to overhead which tends to overwater certain areas while leaving others drier. It works best after the crop is established, as it often can destroy seedlings. Any slope and you are liable to get gullies.

If you are limited to 3 or 4 psi, and wish to conserve water, I suggest a small gas water transfer pump, assuming the pond is too far from electric power. They usually will run a couple hundred. Like a chainsaw, the few liters of fuel it would consume are quite worthwhile in operating sprinkler or drip systems. Perhaps there are now reasonably priced solar pump systems you might find.

If your pond is just established, you might wish to wait a year to get a handle on its seal and evaporative losses. That could point you in a different direction, with some pond evaporative losses exceeding an inch/day.