Are you sure?
IIRC, production of the Tiger took only about twice as long as the PzIII/IV and cost only twice as much to build. (250,000RM)
In terms of combat effectiveness and force projection, I believe those 1355 Tigers were a far greater investment than 2710 PzIVHs would have been. Germany would have been vastly outproduced regardless, but the Tigers allowed the Panzerkorps' best asset (its trained and experienced crews) to engage much larger numbers of enemy armor and have a far greater chance of surviving such encounters.
Also, the Tiger was just as fast as a Sherman (38km/h); and while it was somewhat slower than the T-34 series (50km/h), it was by no means lethargic.
Edit:
Wiki says...
Of course that's by no means the most reliable of sources, but it corresponds to the books I've read.