Now I really only understand #2 and 4, the rest I'm not sure what you mean. # 2, grab it, #4 wood tip woody, or plastic clicky. When I commented on the first video, cus I didn't go further, it sounds like sh*t. There's no definition between hits, he's edging and tip hitting it with no clue what he's doing. It was straight wash and rivet the whole time. Not to mention he does the one thing I can't stand, ever, he lays the stick flat on the snare and does that stupid click, click on the rim. WTF is that ?? I'd like to see him stop and play that ride with both sticks for a few maybe ten seconds, or if he's brave, a minute. Show what it really sounds like. I'm not hating Boss, just commenting OK.
#1 Medium to thin in weight, but with a greater preference for thinner cymbals?
I believe you already know the preference is for thinner cymbals.
#3, A complex and somewhat trashy underlying wash, with controlled overtones, that does not overwhelm the sticking when digging in?
Most of the old K videos that Drumaholic and others posts are examples of it.
#4 A well defined woody or clicky stick.
Woody or clicky does not mean a wood or plastic tip, The terms are used interchangeably to refer to a well defined, non metallic, darker stick sound when playing ride patterns. You can get this with a plastic tip as well although it may be a bit pingier sounding because the plastic has a harder surface. Its more about the cymbal than the stick, although technique and the sticks used certainly play a part. Such cymbals often also tend to have a generally darker, smokey sound and an almost buttery feel to them when playing ride patterns. I can not define a buttery cymbal feel for you. Once you play one, you'll know what I mean.
#5 Limited volume. A good jazz ride should not overwhelm other acoustic instruments, low volume electronic instruments, or vocalists; even when digging in..
In other words, good jazz cymbals are not generally extremely loud even when you dig in when playing ride patterns or crashing. Some are very quiet compared to their hard rock siblings. You want them to serve the music, not shout out "look at me".
#6. Bells should be on the dark side, not overly bright, harsh, metallic, or pingy.
Jazz ride bells are generally darker and don't ring as much as rock oriented cymbals. Cymbals like Old Stamp K's have a dark clunkier sound with relatively little ringing
Not to mention he does the one thing I can't stand, ever, he lays the stick flat on the snare and does that stupid click, click on the rim. WTF is that ??
In the video you are referring to, that technique is called cross sticking and it is a valuable drummer's tool especially during acoustic solos, like from bassists or behind quiet vocals, or for subtle Latin accents for sambas and bossa novas, etc It was originally used as a replacement for a wood block. When appropriate to the music I've used that technique in small acoustic ensembles for jazz and light pop at parties or clubs for close to 60 years. It, like anything else, can be overdone. It is not a technique that one would normally use in rock. Sorry you don't like it. How do you feel about brushes?
Just to summarize there are significant differences between great jazz cymbals and great rock cymbals but, there is some overlap. As an example of that is the new Zildjian Avedis line which transcends jazz and and some styles of rock. I own a 22" and a 20" myself. But the main problem with them is that while they are very good cymbals, they are not truly great for either purpose IMHO. In general the two genres are best served by different cymbals.
Hope this helped.