For a new 5.8m property purchase, the MIP shouldn't be huge. And you do get discounts on the publicly listed MIP rate based on your salary/job etc - so even cheaper.
If you are looking to rent the property out or if you intend to play the "refinancing game" every few years, then MIP might not be for you (MIP is not portable across banks, and you need to pay again for new MIP every refinance).
Remember MIP can only be applied for when you make a new purchase, and not a refi, so if you want more $$ from refinancing from 60% to 80% you are hamstrung. Take the cash now, deal with the structuring later.
The MIP can even be financed. The rebate from the bank also approximates approx 50% of the MIP...
To do a refi on the existing property (with change of owner too?) and to time it all so it works out, sounds like a lot of work (legal fees also) for a 5.8m purchase. There are also more things that can go wrong - the bank funding the new purchase might not approve you for the full amount of the new loan if they also take into account your full liabilities under the old loan being topped up (if you are a joint borrower, they assess you as liable for 100%).