I'm sure Heidi13 will be back with additional detail, but the basic answer is that so much is included in the Viking fare that you would have to pay for separately on Princess that it netted out to a similar per day cost.
Paging @Heidi13 He has detailed information posted on his most recent - and final - experience with a Princess WC. The search function isn't working for me to find a couple of links for you, but if he sees this, I'm sure he'll either provide some details here or steer you to one of his detailed posts.
We did something similar a few years ago, and the hotel on the site, which was called Sanctuary Lodge when we were there, is an experience unto itself. Everything @scotchbonnet says in terms of early and late access, being able to walk up to the top before sunrise and catch it as it comes up, etc., but then also the quality of the hotel itself is 5-star plus.
The Isle of Man is one of our more favorite locations. We flew in for a four-night stay from London one December and thought it was absolutely magical. I understand arriving by sea can be pretty rough, but I know from first hand experience that arriving by air is not usually a picnic, either. Worth it, though.
We did the same, also in 2019, and it was one of our most memorable stops of the cruise. A local gentleman sound us walking back through a neighborhood and invited us up onto his deck for a spectacular view.
If you post over on the Viking Board, several frequent posters have been on one or more of the world cruises, and would likely be very happy to share the specific itineraries with you.
Another thing I just remembered that we always do is to put plastic wrap across the toilet seat and the tank after we've cleaned it. It's a tip that sounded crazy to me when I first came across it, but it keeps the water from evaporating - or at least slows it down quite a bit - so that you don't end up with rings that need to be tackled when you get back. It really does work.
A friend of ours was looking at pictures from a trip to, I believe, London several years back, and at the end of scrolling through the first 3-4 days, she stopped, looked at me, and said: "You did all of this stuff in one day?"
We've noticed this, as well, and my husband is 100% in your camp. We end up 'undressing' the duvet and using the cover as a top sheet, which has to create all kinds of work for the staff, but seems to be the only option. (We always leave a better tip when I've resorted to this!) Occasionally we've been able to request a top sheet and get one, but less than half the time. (It was actually the head of housekeeping at a London hotel who first told us just to take the duvet cover off and use that as a top sheet.)
It sounds like you have a good plan in place, but one thing that occurred to me as I read this post is that - if you're able to do it - you could walk your bags off yourself, rather than putting them out the night before for Viking to offload with all the others. That eliminates the time associated with waiting for your bags once you disembark. (That said, in our experience, the bags have always been waiting for us once we walked into the terminal.)