Instead of patching the source, the Makefile should be patched to use sdl2-config to set LDFLAGS and CFLAGS (instead of hard-coding them), i.e:
CFLAGS := [other flags...] $(shell sdl2-config --cflags)
LDFLAGS := [other flags...] $(shell sdl2-config --libs)
That will set the correct compiler and linker flags for you installation, and you can leave the include as just "SDL.h".