Rich,
I'm not sure, but you might have to enable "Install Unknown Apps" and to do THAT, you might have to enable Developer Options (usually by tapping the build number at least 7 times).
I have a table that has a custom ROM (too slow with all the Lenovo bloatware) and all I have to do is double tap an apk to install. If that doesnt work, using adb might do it as well (never tried, since a quick install always worked).
Unfortunately, the share with all the old versions was taken down once the decision to start charging a subscription was made. Fortunately I saved prior versions up to that point, so I can recover from a reimage. You can also build prior versions of "old"Avare from Githubas long as THAT is still available.
I see also that depending on the browser (and again, probably the "unknown apps" settings) you can put "file:///avare.apk" (or whatever) in the url and it might ask you if you want to save or install. I remember I sometimes would put the apk on a local webserver and get it to install that way with Chrome.