That makes a whole lot of sense. For myself, I wouldn't even attempt this because it's so much harder and more time-consuming to try to reimplement something like bignums efficiently than it is to just use a stable, mature and fast external library like GMP or CLN — or something like your project if BSD/MIT licensing is a must.
It's been done. I think it was Gambit Scheme that had its own bignum library. And for a while, very large integer arithmetic was reportedly faster than GMP, which if you know anything about GMP is quite an achievement. However, the GMP guys subsequently fixed this problem.