The magic configure incantation was:
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# Compile static libraries, and use statically linked openssl (-openssl-linked):
OPENSSL_LIBS="-L$DEPSDIR/openssl-1.0.1c -lssl -lcrypto -lgdi32" ./configure -prefix $INSTDIR -I $DEPSDIR/openssl-1.0.1c/include -confirm-license -release -opensource -static -no-qt3support -xplatform unsupported/win32-g++-cross -no-multimedia -no-audio-backend -no-phonon -no-phonon-backend -no-declarative -no-script -no-scripttools -no-javascript-jit -no-webkit -no-svg -no-xmlpatterns -no-sql-sqlite -no-nis -no-cups -no-iconv -no-dbus -no-gif -no-libtiff -no-opengl -nomake examples -nomake demos -nomake docs -no-feature-style-plastique -no-feature-style-cleanlooks -no-feature-style-motif -no-feature-style-cde -no-feature-style-windowsce -no-feature-style-windowsmobile -no-feature-style-s60 -openssl-linked
OPENSSL_LIBS="-L$DEPSDIR/openssl-1.0.1c -lssl -lcrypto -lgdi32" ./configure -prefix $INSTDIR -I $DEPSDIR/openssl-1.0.1c/include -confirm-license -release -opensource -static -no-qt3support -xplatform unsupported/win32-g++-cross -no-multimedia -no-audio-backend -no-phonon -no-phonon-backend -no-declarative -no-script -no-scripttools -no-javascript-jit -no-webkit -no-svg -no-xmlpatterns -no-sql-sqlite -no-nis -no-cups -no-iconv -no-dbus -no-gif -no-libtiff -no-opengl -nomake examples -nomake demos -nomake docs -no-feature-style-plastique -no-feature-style-cleanlooks -no-feature-style-motif -no-feature-style-cde -no-feature-style-windowsce -no-feature-style-windowsmobile -no-feature-style-s60 -openssl-linked
Nothing special needed to be done for the openssl build:
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./Configure --cross-compile-prefix=i586-mingw32msvc- mingw
The payment protocol code add a couple more depedencies to Bitcoin-Qt:
+ QtNetwork with OpenSSL support
+ Google's protocol buffer library and compiler.