For the vert question, nothing builds your engine for skinning quite like skinning. I joined my local race league this year and while my setup is super heavy by race standards and I'm in no way shape or form near the top of the rankings, it's been really beneficial. It's like speed training days while working up to a marathon. I do a lot of long distance hiking & mountaineering during the summer, so I have the endurance & nutrition/hydration right to keep skinning all day, but needed to increase my pace & turnover. Cranking out 2k of vert with descents & transitions in an hour to an hour and a half on a weeknight has really changed my "comfortable" pace.
If you're not in a spot where that's an option, isolate what's holding you back. For me, it's cardio. For friends, it varies between muscle strength & endurance - like barking hip flexors partway through the day, or skinning technique/efficiency, or losing a lot of time with more technical skinning - like kickturns or spots where you need to side-step without your heels locked in. For others, it's gear that's heavy or boots that don't stride well (looking at your reply to the setup thread, you look pretty well geared-up).
3-5k of vert on your first few tours is totally respectable. It gets easier with practice. The guiding ops near me also do "introduction to touring" classes that teach skinning technique and transition hacks that are meant to compliment an AIARE 1. Might be worth looking into, or I really like doing a day of private guiding every season or two, and the guides always have tips on how to get more bang for your buck with strides or keeping you gear organized for quick transitions. Youtube tutorials help too!