I suspect there may be another way to do this.
I have several domains, and some of them get spammed rotten. I used the ISP's "mail control panel" to set up that the spammed addresses get forwarded to Gmail, which filters them and then sends them to my "secret" address.
Could you not set up your present primary ISP to forward mail to the "Business" address to Mike-Bracknell's server, while anything else goes to your normal POP-server?
You would then have the multi-access thing working fine. Mike would only see mail for your Business address, and all would work as you require.
I do something vaguely similar with one of my accounts, which is set up as an Imap address on Gmail. That works for my purposes, but may not for yours.
I'm very much with him on not messing with PST files - they are a nightmare. I don't use Outlook for mail (Thunderbird does what I want far better), but I've had all sorts of problems with calendars and address books in PST files.