"Tail Heaviness" in terms of physically lifting the tail doesn't say much about the aircraft in the air. All it says is that its a heavy aircraft, and that possibly the main gear is relatively far forward of the C.G. The Helio Courier comes to mind
About fifteen years ago I converted my Cessna 150 Aerobat to a Texas Taildragger with the long gear on it.
That sucker sure was tail heavy due to how far forward the main wheels were.
The biggest problem with such a configuration is controlling yaw during take off and landing, but it did what I wanted it to do, it made for a good little tail wheel trainer because it was demanding on the runway.