Tetrasodium pyrophosphate

I would be a little surprised if you could get your hands on food grade tetrasodium phyrophosphate(TSPP), but maybe you're a Sigma-Aldrich employee or something...

TSPP is commonly used in commercial food applications to inhibit bacterial growth, especially where animal proteins are present. http://www.ncbi.nlm.nih.gov/pubmed/22934995 This phosphate is also found as an anticaking and conditioning agent in dry vanilla pudding mixes, although my personal experience tells me that the TSPP may be acting anticaking/conditioning in marshmallows, but it's more likely that it is inhibiting bacterial growth since many commercial marshmallows use gelatin(animal-derived) in their recipes. http://pubchem.ncbi.nlm.nih.gov/summary/summary.cgi?sid=24898899

I would also like to posit a partial reason for why your home-made marshmallows are not behaving the way you expect.

First, the industrial process(ultra precise & temp controlled equipment) is probably yielding marshmallows that have less water in them, creating a more dense and solid marshmallow.(lowering the water content/activity of the food means that bacteria will be less likely to set up colonies on your food product). Yay, technology, Second, the marshmallows you are buying from the store have probably been sitting around for a while...like A WHILE, meaning they have lost a little bit more water from transit and storage before getting to your grocery shelves. I believe both of those situations contribute to the textural and roasting difference. Less bound water in marshmallow = more similar to commercial product. More bound water in marshmallow = more melty...faster.

So your question was HOW do you use TSPP in recipes...were you to possess some...

I would incorporate an amount into the water before you hydrate the gelatin. There is an LD50 listed on the pubchem resource I provided, as too much can be detrimental to human health. As for how much you should add...I won't voice any advice on it.

What you might try, is using invert sugar in your recipes if you can source that (much easier to do, and doesn't require any hazard chemical shipments), or trying to get rid of more water through your heating steps in the recipe, and finally by letting your finished marshmallows dry out a bit after they have set up. If I had that kind of time, I would turn them out onto a fine-grate cooling rack and covering them with cheesecloth to accomplish drying the final product.

Good luck on your endeavors.

Gelatin takes ~2weeks to fully set to it's final texture, and before then it will melt more easily, as the gelatin molecules are not "fully locked" in position. TSPP is used at an extremely low rate to help Gelatin set quicker, it has been termed " vitamin pills for Gelatin" buy an old Corn products syrup expert who used to tour the world helping folks, he had been in the business for >40 years, and that was ~20 years ago. I have consistently used it to help set gelatin faster in mallows ever since, though a modified starch also helps, but cannot be used unless you cook under pressure (pressure cooker may work), all granules must be swollen, and none burst for best results.