GWD 23-23 关于while 和 but的区别及省略问题

After several years of rapid growth, the healthy care company became one of the largest health care providers in the metropolitan area, while it then proved unable to handle the increase in business, falling months behind in its payment to doctors and hospitals.

A.while it then proved unable to handle the increase in business, falling months behind in its payment to

B.while it then proved unable to handle the increase in business and fell months behind in its payment to

C.but then it proved unable to handle the increase in business, falling months behind in its paying

D.but then proving unable to handle the increase in business, falling months behind in paying

E. but then proved unable to handle the increase in business, falling months behind in paying

OA:E

这道题目研究和很久还是有些疑惑.很多讨论直接排除了A/B/C/D选项,因为A/B/C/D中均没将prove 的被动含义表达出来.
同时认为E中省略的BE动词,所以仅有E是正确的.
根据but的平行及省略原则,是否看出这里是省略了became, 而proved在but句中是过去分词做表语?????
有点晕,烦求哪位NN出来解释下? 谢谢了