Pressure washer to clean out debris.

I tried using a pressure washer with some success in some areas. But the force required to clean most of the blockage destroyed the wood, so I didn't proceed.

Run circular saw between boards.

That is an interesting idea. Have you tried it?

I used/use a putty knife. Dog hair, redwood tree debris, pieces of chewed wood.

Couple times. Blade needs to be rip tooth at max depth and STOP before cross pieces deck is nailed/screwed to,you don't want to cut them. If skips bother you,raise blade to exact thickness of deck boards and clean them. The reason for having blade deeper than boards are thick is saw tracks better,safer due to less kick-back and requires less power from motor (common knowledge amongst those who often rip boards with hand held saws).

I'd use a multi-tool with an oscillating blade. It will be easier to control than a circular saw, pose no danger of kickback, and has a thin kerf, so you won't be doing much, if any, removal of the deck wood.

That is an excellent idea. I was trying find a thinner circular saw blade without much luck, great suggestion!

To Klem1 - your suggestions are very useful and I appreciate your advice about setting the blade depth greater than the board width. Thank you,

Please understand saw blades are designed for specific tasks. Rip blades have larger teeth and greater set which in turn creates a wider kerf and this isn't a job where you should go against best practice. Thin rip blades are available but they aren't suitable for doing what you need here. Thinner blades begin wobbling due to heat from friction sooner than thicker blades and continous cutting on this task will create a lot of heat. Don't get hung up with trying to preserve one or two thirty seconds of lumber ,there is no reason to. If you are inexperienced with power saws for goodness sake don't cut your teeth with this job,use hand tools and sweat rather than bleed.