Is there an open-source / free official Myers-Briggs assessment I can adopt?
The IPIP may provide what you are looking for.


  This IPIP Website is intended to provide rapid access to measures of
  individual differences, all in the public domain, to be developed
  conjointly among scientists worldwide.


In general, the scientific literature tends to focus more on a dimensional approach based on the Big 5 model of personality than the type approach. There are strong correlations between MBTI and Big 5 measures. 

The IPIP website provides measures of the Big 5. The following table from Furnham (1996) summarises some correlations across a few studies between the NEO Big 5 and the MBTI.



You can find a listing of some of the multi-construct measures including Big 5 measures on the ipip website.

References


Furnham, A. (1996). The big five versus the big four: the relationship between the Myers-Briggs Type Indicator (MBTI) and NEO-PI five factor model of personality. Personality and Individual Differences, 21, 303-307.