tar xvzf ejdk-8u...
./opt/ejdk-8u111/bin/jrecreate.sh --dest /opt/jre_builded
chmod +x /opt/jre_builded/bin/java
ln -s /opt/jre_builded/bin/java /usr/bin
Apparently including the lib/arm/libawt_xawt.so file from another distribution (like the already headful HardFP one) is enough to tell Java to not be in headless mode anymore, and to properly load the awt library.
ARMv5/ARMv6/ARMv7 Linux - SoftFP ABI, Little Endian 2
ARM v6/v7 Linux - VFP, HardFP ABI, Little Endian 1
lib/arm/libawt_xawt.so
/opt/jre_compiled/lib/arm/libawt_xawt.so