Please Ignore ignorant advice...
As far as the compost, do it! Sunshine mix, if I am not mistaken (I have never worked with it) is a peat-based mix, with very little or no nutrients. Compost will do wonders for your plants in this case. Does the compost have any information included? Do you know the NPK??? It is probably a high-nitrogen compost mix, especially if given this time of year. Try to mix it in with your Sunshine mix, and if you can get some Guano.... do it. It is not a bad idea to get it in your initial mix, but it also works well as a top dressing for flowering (sprinkle it on top of your soil in mid-late summer/early fall) and in teas. I am speaking of course of high-phosphorous guano; but high-nitrogen guano is a great soil amendment as well. It can be a great substitute for blood meal as well, as it does not attract animals.
So, as far as the compost goes, I would say go for it! It is hard to burn your plants with most organic nutrients (although it is very possible with many), so you probably can't do harm with even the hottest compost blends.
S-Town