Wouldn't they have been better off giving up the production of over-engineered tanks and stuck to mass producing Panzer 4's and Panzer 3's?

Not really. However, before I get to that, I would like to point that the Germans continued to produce Panzer 4's until the end of the war, and the Panzer 3 became obsolete late in the war.

Having said that, there are two main things to consider.

(1) By the time the Tiger (Late 1942) and the Panther (Kursk) especially were introduced, Germany's outlook was bleak. The Germans needed to finish off the Red Army in 1941 or 1942 at the latest, and when that didn't happen they found themselves embedded in a war of attrition against an Alliance that Germany and her slender resources could never hope to defeat.

The Germans generally opted for quality over quantity. From a production standpoint, the Germans were never going to come close to matching that of the Allies. Superior quality was the only chance they had to overcome the that disparity.

(By the end of the war, the US, Britain, and Russia had produced ~256,000 tanks, where as Germany and her European Axis partners only managed slightly more than 70,000.)

https://en.wikipedia.org/wiki/Military_production_during_World_War_II#Land_forces

(2) Oil. Germany didn't have it late in the war. Which would be another reason to opt for the quality over quantity (granted the Tiger's fuel consumption was abysmal).

If you're familiar with the Battle of the Bulge in 1944/45, part of the German plans relied on the successful capturing of Allied fuel depots. When that failed, large numbers of tanks had to be abandoned in the field. (A tactic that Rommel had success with a few times in North Africa).

Nonetheless, the point is that often times it wasn't a lack of production that was a problem late in the war, but rather a lack of oil and trained men.