I've used drip systems with excellent results. The style I used had a limit of 25 PSI for the flow rate to work right. I dont think you'll have a problem with the pressure with a small pump. If needed, a pressure regulator can be installed in about a minute with a cost pf maybe 20 bucks.
I've got
sandy soil. I set up my system with drippers every 2 feet. A 4x50 bed would require 2 rows with 25 tips each, or a single line down the center with foot long 1/4" tubing every foot. The advantage of the tips on the end of a foot of tubing is moving them around when a different crop goes in.
At the spacing above, the 2 beds would require 100 drip tips. With a flow rate of 1/2 gpm/tip, that vessel will drain in 5.5 hours of use. For my environment that would get me by for a dry week.
Before I used drip, I used
clay pots with excellent results. I was in a D2 drought at the time and those pots would empty in a day or two. Filling them was getting to be a chore and the plant growth was making it hard to find the pots. I ran a drip line down the center of the beds with a drip tip shoved into the clay pot and a timer on the faucet. Every other day the pots would be filled automatically.
I did the math on flow rates, don't know where the notes are, but as I recall a 25 PSI supply would service around 250 tips rated at either 1/2 GPM or 1 GPM.
If you drained the entire 275 gallons across the 400 sqft, it works out to the equivalent of .8 inches of rain. About enough to last you a week in well drained soil, perhaps 2 weeks in a heavy clay soil.
John Wolfram points out the algae issue. I gave up on the drip system because of the clogging problem, and I was using city water at the time. An inline filter may be needed. Another option is an aerator and some algae eating fish.