Another possibility to consider is 次第

> as soon as; immediately (upon)often after the -masu stem of a verb

(source: jisho.org)

E.g. 

> 受け取り次第
>
> (Immediately) after receiving

which would definitely be a more appropriate thing to use in say, a business setting and with less strong demand-like emphasis than なる早 or なるべく早く