Rip old door in half?
It might work - however the problem would be where the centre uprights join the horizontal sections.

This piece of ascii art might help:

||========||
||   ||   ||
||   ||   ||
||   ||   ||
||========||
||   ||   ||
||   ||   ||
||   ||   ||
||========||


Where "||" is the vertical sections and "==" the horizontal.

You'll end up with two sections like this:

||====    ====||
||   |    |   ||
||   |    |   ||
||   |    |   ||
||====    ====||
||   |    |   ||
||   |    |   ||
||   |    |   ||
||====    ====||


As you can see buy cutting up the centre you are cutting through the middle of the joints which will weaken the joints and they could come apart.

These joints are mortice and tenon and you could try strengthening them by putting a dowel through the tenon before cutting:



Drill all the way through, insert the dowel (with glue), plane and sand smooth. If you're painting the doors you won't see the join. To drill the hole straight you could use a portable drill guide or a plunge router.