Well I finally got around to building an APK and it was not fun. Not at all.
Firstly, it seems to be impossible to use an older version of Studio. Sure, it will install but as soon as you run it bitches about all sorts of dependencies and clashes and the only way to get it going seems to be to upgrade to the latest version. The only way I could find anyway.
So you upgrade and first remove the old version but the built in removal is not that clean and there are residual settings and stuff lurking around that throws the new installation. Try again but first root out all those residuals manually and finally, after about an hour of crunching and downloading, a working version of 3.2 emerges.
As far as the actual installation is concerned, I simply accepted all the defaults because I felt too ignorant to start fiddling with the various components. As a result I suspect that a lot more is now cluttering up my hard drive than one actually needs to simply compile and build an APK. A bit of detailed guidance on the installation process would not go amiss.
Relative to Chucks original instructions quite a lot seems to have changed in the new version of Studio. It talks about bundles and there are a bunch of rather confusing options.
What worked for me was :-
Generate signed bundle/APK
APK for a device
Build type "release"
V1 Jar signature
Then, first attempts at a build failed repeatedly because the build process wanted, but could not find "list-gradle-26.1.3" even though it had 26.2.1 and api-26.1.3. This was eventually overcome by editing the Mintoris generated master build.gradle text file (found in the root of your project directory). Changed the last part to also look in Google, as follows :-
And behold, an all singing, shining, dancing, polished APK emerges.
With a bit of luck it will all be pretty simple from now on.
Hope this helps anyone else experiencing the same problems.