I never knew anything about equivs -- you are way over my head with that process. For fun, I installed equivs and tried your commands on my VM, and crashed and burned with the "equivs-build qtbase-abi-5-3-1". From the error messages, there are obviously a few more things to know about when using equivs. But it looks interesting.
EDIT: OK, read about editing the config file to show the package name, and then it works as you said. I installed both the plasma-desktop and the kde-full packages, and lightdm now logs me in as expected/hoped for. Probably not the most rugged KDE system on earth, but not bad for playing around and doing experiments.
Thanks filhocf!