I have now learned that iTunes does NOT like AAC encoded files, unless they are within an MPEG-4 container and written as file type .m4a (upper or lower case). Files of type .aac are generally ignored by iTunes - in Windows at least.
Thanks for the suggestion to use dBPoweramp's Music Converter.
I tested about 15 audio format converters, mostly under Windows, some under Linux. dbPoweramp was the most convenient to use, with the added advantage of providing the Fraunhofer Institute FDK-AAC encoder - which those who appear to know claim to be the best aac encoder. The disadvantage of this software is that it is not free and is quite expensive for what really is just a GUI around the free ffmpeg encoder.
An almost equally good format converter is fre:ac, available freely (and at no cost) in both Windows and Linux versions. The windows version has the advantage of automatically picking up Apple's Core aac converter if iTunes is also installed on the computer. It also has a lot of configurability which some other apps. lacked. I will probably revert to fre:ac after the dBPoweramp trial period expires.
For others who might be experimenting with reviewing audio converters, I would raise the strongest possible warning about the SUPER converter by Erightsoft. I did manage to avoid the half dozen or so unwanted items of software it was determined to install on my system but could not avoid it seriously hijacking my browser (which HIJACKTHIS could not recover) or from installing 1173 (yes, you read that correctly) infections on my system. Malwarebytes managed to remove these but I was advised to re-install Windows after a full (not quick) reformatting of my hard disk. I have now done this and have learned a painful lesson, since re-installing Windows also wipes out the Linux GRUB loader.