Will a 04/05 Z4 Gearbox fit E34?

Very much doubt it! They're both electronically
controlled by an ECU which will be very different,
plus the Z4 will have traction control and other bits. It
should physically bolt onto the back of your engine
but who knows if it's the same length or if the
propshaft will bolt on.

If it's any use, a mate of mine has broken up a 1993
525i Sport with a good autobox. It won't be dear but it
has done 200'000 miles! But they either work okay of
they don't and this would be a cheap way out for you.
A local BMW specialist I know could fit it for you as
well.