I think it is a good idea, with some caveats:
Would it be ok if just one person emailed Chi & Brad when they thought something was close, or would it have to be agreement by committee? We're probably not all on here enough to do the latter, or to reach agreement by discussion.
In regard to the above, in my opinion submitted reviews that are close to primetime (great phrase) already jump off the page and their quality shines through (see Ercoman's reviews last year, for example). Hence I think the process would work if any one of us reads a review like that and sends an email. Obviously Chi & Brad are the gatekeepers and it's then up to them.
Also in regard to 'nearly there' reviews - we're not writers obviously, so with these reviews I don't think it is helpful for us to offer minor edits - it would be better to send the email and let proper editors do that. I don't know how much editing you do for your regular contributors but I expect there is some. Brad and Chi would just have to trust us that we are sending through something that is not a mess but nearly there.
Obviously the majority of contributions need a lot of work so we would try and help out there, provide some pointers, and keep them away from Chi & Brad.
Feedback: I wouldn't want any personal feedback after the mail is sent but by the same measure we couldn't guarantee the writer any feedback unless Chi or Brad then popped in to do that.