Schengen visa for quite a unique case

I was recently hired as an intern in the UK for 6 months, with an opportunity to make it permanent if both parties are happy at the end of the period. As the company I work for is heavily involved in the travel industry, I will need to make frequent trips to the Schengen area to visit properties and guests.

As my UK permit is 6 months, it's apparently not long enough to be able to apply from the UK, so I will have to return all the way home to South Africa to apply for a Schengen visa.

I recently graduated from a Swiss university in July of this year, and I just started my job in the UK this month. So no bank statements yet, no payslips yet, and my serious concern is that the visa officer won't be convinced of my ties to home. Essentially, if I don't get the Schengen visa, my boss has to replace me.

My visa performance record is pristine. I've had a Swiss residence permit for the past 4 years, I have a U.S. visa expiring in 10 years, and have made many trips to Schengen countries in the past. I've never overstayed a visa, been in any trouble or any of the sort.

What things can I show to convince the visa officers that I'm a safe bet, and have no intention to stay?

I'm planning on attaching my graduating certificate from the prestigious Swiss university to substantiate the fact that I'm not willing to throw away my future away by overstaying my visa.