There’s a whole thread about the issue, which led to a process being created to temporarily increase limits for online payments, but I’m not sure whether a similar process applies to CHAPS payments.
I was able to successfully test that process in September 2018. However, I’d urge you to contact them by phone, as others have suggested. I very much hope and expect that they will meet your expectations, but it feels to me like you need to have this reassurance in advance.
Do please confirm back to the forum once you’ve completed your transaction, and let us know how it went.