My strategy would be based on the premise that, by December 1944, the war was no longer winnable by Germany. My first option would be to negotiate surrender terms, but the question asks us to assume that peace is not an option. My next option would therefore be to concentrate most of my resources on the Eastern Front, while leaving just enough forces on the Western Front to maintain token resistance (and to fulfil the question’s requirement that I keep fighting).
The purpose of this strategy would be to delay the Russians as much as possible in the East, and to make it as easy as possible for the Anglo-Americans in the West to overrun as much of Germany as possible, while still maintaining the pretense that I was resisting their advance. My rationale is that most Germans (both civilians and soldiers) would be better off falling into the hands of the Anglo-Americans than those of the Russians, given how revenge-driven the Russians were for what they had suffered under German occupation.
This is in fact pretty close to what the German Army actually did in April and May 1945 as the war was ending: giving people as much time as possible to make their way towards the zones which had been defined for Anglo-American occupation after the war.