Is the normal Tangram construction truly so good that all others are not worth trying? If so, why, but the premise seems unlikely. At the very least I would expect there to exist many other constructions with their own pros and cons compared to the classic. Contrariwise, though, I am unable to find a single alternative construction.
Here is the classic construction for reference followed by some alternatives I’ve been thinking about, though I was certainly not the first to come up with these designs given the Tangram’s long history.
The Classic Tangram Puzzle:
Many other possibilities exist. I think using the tetrominos or tetrahexes could provide interesting possibilities as well.