Regulation Z allows you to use the CD to reset tolerances in the event of a changed circumstance. If you believe that you have a changed circumstance (and it sounds like you do) then you would be able to use the CD to reset the tolerance.
A helpful excerpt from the CFPB’s SECG (see sections 10.2, 11.11, 12.2, 12.3):
Like with a revised Loan Estimate, a creditor can use a corrected Closing Disclosure to reset tolerances when there is a changed circumstance or other triggering event. (Comment 19(e)(4)(ii)-1)
The three-business-day waiting period requirement applies to a corrected Closing Disclosure that is provided when:
The loan’s disclosed APR becomes inaccurate;
There are changes to the loan product; or
A prepayment penalty is added to the loan. (§ 1026.19(f)(2)(ii))
If other types of changes occur, creditors must ensure that the consumer receives a corrected Closing Disclosure at or before consummation. (§ 1026.19(f)(2)(i))