So I've played a fair amount of new Kayle now
At a couple different skill ranges, and I've got some updates on how she actually fares.
Bottom line, she's definitely worse off early game than prior to the rework and has basically no good solo lane matchups. She's probably best off in a funnel, the one game I ran of that went very well indeed. But she does have some lanes she can kind of manage before turning it around. I asked some challenger players a couple questions, Azael had some insight on more than one podcast, and I'm beginning to get a picture of how she can be played effectively.
As a solo laner what I've had the most success with is running klepto and basically using it off cooldown for "poke" (more like tickle) to spam up the gold advantage and hit item breakpoints a bit earlier. Usually I run free boots or free stopwatch, minion dematerializer to control the wave, and I'm fond of time warp tonic for the staying power and on demand move speed buff. Usually sorc secondary with mana flow band, and then transcendence, gathering storm, or celerity are all fine in different matchups.
Personally I like putting 3 points in q for q farming early before maxing e, but most high level players are really liking to max q first. Some max w second, and I usually get it to level 3 before finishing my q, but for me her ability max order is pretty flexible depending on in game situations and I don't feel tied to any set order game in and game out.
As far as builds go I've tried her in just about every possible configuration (man I do love me some hybrid champs), but I've had, by far, the most success when I rush a triforce on her. With klepto you can easily get this in around the 12 minute mark and her trades are really quite good with a sheen proc early. Typically I follow that with a blade of the ruined king and at this point I'm usually feeling pretty capable in skirmishes and team fights. I'm starting to consider these 2 items core on new kayle. After that I've really been liking hourglass to free up my ult for spam on an initial engager. I feel like GA, hurricane, I.E., merc scimitar, ludens, rab cap, nashors, rage blade, and even frozen mallet or rylais are acceptable items as well and the build path can really be tailored to the specific game. Boots can also be mixed and matched for build based on situation.
She's quite fun to play once you figure out how to play around how awful her early game is and I rather enjoy having a champion that I can build in a number of ways to be effective depending on game. She's certainly more viable than I first thought, but her win conditions are indeed pretty narrow and it'll take practice to figure out when you can and can't play her effectively.