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I'd use 8' nozzles on both sides of the strip

yes 8' spacing on both sides of strips

4- 8' quarter sprays
16- 8' half sprays

total gpm=9.36 gpm using Rainbird nozzles.

I'd put all 20 heads on 1 zone.

Seems like one of the things I've seen in this type of situation was to use triangular spacing. Start in one corner with a quarter sprayer. Move down the strip about about 4' and place a half on the opposite side. Move down another 4' and swap sides again. Continue going until you place a quarter sprayer at the other end of the strip. (In your case, use an interval of about 3'10" so that your last half spray doesn't get located 2' from the end of the strip).

The layout would require 17- 8' half sprays and 2- 8' quarter sprays (same gpm because you wind up subing one half spray for two quarter sprays).

Once upon a time, there were strip nozzles that could be spaced in a line down the middle of your seven-foot-wide strip, but those were brass nozzles no longer manufactured.

I know that I could effectively water that strip with eleven 8-foot nozzles. On one side would be quarter circle nozzles in the corners, with four more half-circle nozzles spaced in between. The other side would have five half-circle nozzles. The distance between nozzles would be fourteen feet. Not exactly textbook spacing, but the lawn would never know the difference.

Modern popup heads allow you to run many of them on a zone. Only in extreme circumstances would you ever worry about how many heads were in a zone - the total flow through the nozzles is what you'd consider.