In some cases, like with Mozilla's Firefox mobile browser (also tested in Chrome), you can request that the "Desktop site" be shown; that workaround allowed me

In some cases, like with Mozilla's Firefox mobile browser (also tested in Chrome), you can request that the "Desktop site" be shown; that workaround allowed me to choose different songs. There are also a couple of pages that seem to have a copy of the com.earslap.touchpianistapp APK, but I can't vouch for any, as I don't have a disposable mobile with which to test at the moment.