Getting around company insurance policy

I've got a business trip in a couple of weeks and it looks like the perfect
opportunity to 'beat' the airlines, get some great x-country time and apply
my license in a practical way.

I need to get to Houghton in the UP of MI from Chicago. It's basically 300
miles due north: ~3 hours in the 172 rental. 4 hours door to door max.
(nasty winds, TS's, Tornados aside)
In the airlines, I have to fly to Minneapolis first which works out to ~ 500
miles, 2 flights and ~7 hours door to door.
The rental cost is a little more expensive but I've no problem paying the
difference - So, let's go...

....Our company handbook explicitly states that the use of private aircraft
is not allowed. So I asked if I could get a waiver and the answer back from
the insurance company was a "Big No".
As far as the FAA is concerned, it's fine for a PP to get to a place of work
this way.

Anyone found a way around this that'll keep everyone happy?

thanks

Iain