If the problem is hard water, some soaker hoses clog up very quickly with minerals. Maybe even faster than drippers!
If clogging is the problem, the more expensive "pressure-compensating" drippers are also more resistant to clogging than non-PC drippers.
Some people have made "mega drippers" out of old garden hoses, by drilling 1/8" or 1/4" holes, and then only running water into it briefly. But that would distribute water less evenly than a drip or soaker system.
Really, I don;t have any good idea, or knowledge of specific soaker hoses or netafim. What is netafim? If that's dripline or drip tape, yes, GREAT, that is what pros use if their rows are long enough.
Personally, I would always choose a dripper product over soaker hoses, just because I believe that a dripper CAN be designed to resist mineral clogging, and to be cleaned, but soaker hoses are totally vulnerable. Plus, the only soaker I ever bought always stunk of rubber, and I didn't like thinking that I was feeding those stinky chemicals to my plants.
BTW, I like your choice of raised bed geometry. Four feet wide is as wide as I would go, myself, but I have fairly short arms.
>> I'm not wanting to waste water through wind or evaporation
Usually that causes people to use drippers or soakers. (I guess people who can laser-level their entire field can use one-time flood-irrigation, but not with raised beds.)
Sprayers are hugely wasteful because of the small drop size. The drops and mist blow all over Creation, and also evaporate rapidly. You would waste somewhat less water with larger drops, such as thrown by mini-spinners instead of sprayers. But you would still waste water on over-spray, and some to wind and evaporation.
All I can think of is a clumsy variation on flooding a field once in the spring. If you have lots of time and water is very expensive, you COULD hand-water each bed, but not using a "shower" or 'spray" hose nozzle. Water infrequently with a hose with NO sprayer, so the water just pools on top of the soil and perks in after you've walked away. I think that has other drawbacks, like uneven watering, but it might be possible to do it without much water evaporating.
Your clay hardpan should keep the water from disapearing straight down as it would in snady soil.
Are you interested in games with half-buried soda bottles or unglazed clay pots buried in the root zone?