I once had a site with 6k daily google organic search traffic. I decided to overhaul the entire website and put up a new platform. I 301 redirected all of the previous pages back to the homepage and put the new platform in a separate directory. Google quickly ranked all of the new pages in the new directory and my daily organic search traffic went from 6k a day to 35k a day under the new platform and the 301 redirect.
With my experience in that project, the 301 redirect to the home page does work. The 301 redirect to the home page was done in late 2016 and the 35k traffic began happening in early 2017.
I did find that the inbound links to the previously ranked pages did effect the traffic to the new platform. For instance, if my site was previously about "cupcakes" and my site was now mostly about "strawberries" and most of the old links came from "cupcake" websites, after the 301 redirect to the homepage, Google sent more traffic to "cupcake" pages on the new platform than they did to the "strawberry" pages on the new platform. Even though I was clearly internally linking to the "strawberry" pages much more.
If you do a custom 404 not found page with a single link to your homepage through your logo it should pass some link juice to your home page. Google will likely deindex and derank the 404 page which will diminish your link juice.
The best method is to create relevant content on that 404/deleted page in relation to the links that are linking to it and its previous history and keywords in the URL. By keeping a great page up on the deleted page, it will retain its ranking and your link juice and Google trust will be much higher.
My recommendation is to first try to create valuable content on the deleted pages with a link to your homepage in the logo. If you can't do that, then do a 301 redirect. And if you can't do that, do a 404. Though frankly, I'm not sure if a 404 or a 301 is better. I can only talk from my own recent experience in doing the 301. The 301 worked.