You haven't really said why KDE will not install. From what you wrote you were on the right path to getting it installed. Use kubuntu backport then install kubutntu-desktop, etc.
I just upgraded a system to mint 19.2 and then installed KDE on it successfully. The second one I have done.
There is an issue though. An old version of a package creates a conflict because it is no longer maintained by Mint and KDE needs it installed.
The package software-properties-kde (0.96.x) in Linux Mint 19.x creates a conflict with mintsources (1.8.x).
The way to resolve this properly is to install software-properties-kde (1.8.0 or greater). This can be obtained from UbuntUpdates.org: Download 1.8.0 package for Tara here (Tessa version 1.8.4 also available): https://www.ubuntuupdates.org/package/m ... erties-kde
The 1.8.x version contains almost nothing and depends only on mintsources being installed. Thereby eliminating the conflict for Mint and allowing kubuntu-desktop and other software to install correctly.
I have fixed a system that had this exact problem, where I forced the old 0.96.x version in only to have an issue with mintupdate constantly wanting to install mintsources 1.8.8 (in Tina) and remove kubuntu-desktop! Installing software-properties-kde 1.8.0 with dpkg gave no errors, then trying mintupdate again it installed mintsources without conflict or asking to remove kubuntu-desktop.