Okay I solved it. I was installing qt stuff from apt-get in a daze and I ended up with Qt4 Assistant, Designer and Linguist. In Qt Designer the qwt widgets were present and worked fine. I looked at another custom widget which was a blinking led and it would not compile either - it also had the Unknown module(s) in Qt Designer error.

So I did some research and found that I was missing qttools5-dev package. I installed it, and the led widget compiled. I tried compiling qwt and this time it worked. It took like 30 minutes on the BBB but it finished correctly. However make install put the libqwt_designer_plugin.so file in an odd place: /usr/plugins/designer. I tried exporting that as QT_PLUGIN_PATH but it didn't work. I copied the file to a bunch of different places but only after putting it into /usr/lib/arm-linux-gnueabihf/qt5/plugins/designer did it finally work. The qwt plugins appear in Qt Creator and everything works. Whew! Thank you for a great product!