No one could accuse you of not having a go, that's for sure!
I thought that i would try and emulate your efforts to see if i got the same results as you.
qmake made a Makefile but that was as far as i got.
so... i looked at the Makefile to see what i could see and noticed the variable QTDIR being mentioned all over the place.
'The penny dropped' as i realised that there were now 2 versions of Qt installed.
qmake -query "QT_INSTALL_PREFIX"
This confirmed my suspicion that the wrong version of qt was being used somewhere along the way.
Well to cut a long story short...(this post is getting too long)
now make works(at least it did for me