Interestingly, when booted up Puppy Linux tonight, the boot was fast, and a standard Puppy desktop with program icons opened.
So apparently the desktop issues, black screen, etc. reported earlier was only a problem in the fiirst boot, after a Berryboot install. Programs seemed to open fast for the most part, afterwards.
I did check out cmdline.txt with the existing Puppy install and it would be straightforward to change the root partition to a USB drive, and copy the partition to a device there. I had already done that for my Raspbian install and I boot to a USB HD normally.
However a major drawback for me with Puppy was discovering that the default browser was Chrome. Totally unexpected and unwanted. Because of the problem reported earlier with the package manager, I didn't explore what alternative browsers are available. I'd have liked to try IceApe just to get a comparison with the same browser on Raspbian, which I had tried earlier. Unfortunately I've heard that support for Iceape has been discontinued by Mozilla, so it doesn't look like a viable alternative, anyway.
I don't know whether Epiphany, as used by Raspbian would run on Puppy. But it's not something I'd probably use much.
I was hoping in Puppy for a browser/email combo with better security and privacy controls -- like Seamonkey on standard Puppies. The Seamonkey WYSIWYG page editor was pretty handy, too. But I guess that isn't available for ARM based computers in general, and not just a specific Puppy (or Raspbian) fault. In fact I don't consider it a fault at all, just the nature of what's available for the platform.
I will say Chrome was irritating in the extreme. It would constantly warn that Ixquick's search engine didn't have a proper certificate, wouldn't display the text of Ixquick search results, wouldn't allow https with the site, and wouldn't allow me to make Ixquick the default search engine. It also had extremely limited adjustment for user preferences. Definitely not my cup of tea.
This has made me re-think what I want to do with the Pi in general. I still enjoy it. It's a cool little board. It's probably going to be used for fun and, for utility sake, ultimately end up in a CNC mill running Grbl controller in conjunction with an Arduino, or if possible LinuxCNC.
It's funny, application issues aren't what would have discouraged me from continuing to work to improve Puppy on the Pi. But the availability of a secure private and highly configurable browser is. That goes for any OS.