Section 3 of "Fast Recursive Division" [1] describes an algorithm for division without remainder which may be faster than the related division with remainder algorithm which was implemented as the fix for JDK-8014319. This algorithm, described as Algorithm 5 on page 14 of the paper, should be investigated and, if deemed worth the effort, implemented in BigInteger.

[1] http://cr.yp.to/bib/1998/burnikel.ps