So I've done a ZC upgrade one time and personally never care to do it that way ever again. It was almost 4 years ago when ZC 1.5.0 was available and I was pgrading from 1.3.9h. I reviewed the documentation, modified every file that was identified as changed, deleted each deleted file, added each new file and went through each override file to be sure they contained the latest enhancement(s). I had originally installed the software with an auto installer to get all the base setup going (mainly to get the database part addressed) and then was in the process of replacing the files with a set from this website when I discovered that the host was behind the times...
The site while online was not heavily trafficed and while that upgrade process did momentarily take it offline, I'll just say that it was far more trouble than it was worth especially with so many other tools and easier ways to do this. Every other store that I have worked on since then I have done by rebuilding the site to provide an upgraded verson (hence the use of upgrade/rebuild as it provides an upgraded site by rebuilding it.)
As far as the above discussion, I don't believe I was the center of the discussion of needing to either upgrade or rebuild. But I would say easiest to rebuild, generally speaking. Either way, the database is addressed through the same basic process... Further, the previous installation of other plugins generally will not prevent the operation of that store when using core files only... Sure certain features and options won't be available at that time but the store will still operate...
Basically and generally speaking, the database modifications made by your other plugins will not negatively affect the upgrade process of the database. Of course the other plugins will have to be updated and their data appropriately addressed to prevent losing that data if it can not be easily reapplied, but they too should be able to be installed/upgraded without data loss...
So, how does one upgrade the database? like you indicated, upload the zc_install directory to the store, then access the zc_install directory. You will need admin profile credentials to be able to do the database upgrade. You will (should) see notices that your configure.php files are not writeable, this is not a problem and actually is a safety measure to prevent you from completely deleting your database.
As for drop tables, that is an option when working in phpmyadmin. Drop tables as is will literally drop all of the tables from the database leaving an empty location that can be accessed, but has no "individual" data other than the overhead to have a database...
I'm pretty sure that your head is already swimming from all of that, but... Wondered why I might have stopped where I did in explanation? Well that individual didn't express the need to know anything further about the process and seemed to be well on their way to what they needed/wanted... Believe it or not I do try to not write a book at every post. :)
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