I think that the podcast is overcomplicating a very simple process. With a mini-mash, you are just trying to convert the enzymes in the small amount of grain you are using but in the end, the extract itself will always be the major supplier of the fermentables.
I remember when I first started brewing the More Beer instructions that came with the recipes said to throw the bag full of grains into your pre-boil water and simply remove it before the water starts to boil. I would certainly NOT recommend you do that but you have to admire their simplistic approach.
I would try to treat mini-mashing just like I would treat a single temp infusion all-grain batch. Using the ratio of 1.25 to 1.35 gallons of water per 1 pound of grain, fill your kettle with the calculated water amount, bring temp to about 150 - 155, add grain bag, and hold temp range for 30 minutes. When the 30 minutes is up, remove the bag, add the rest of your pre-boil water, and bring to a boil, add extract and hops as required.
I understand that the podcast is trying to get the most fermentable sugars from the mini-mash and then they are trying to denature the enzymes but is all that really necessary for a mini-mash? I don't think so. Will it make a significantly better beer? I highly doubt it since the majority of the fermentables come from the extract, not the grains.
EDIT: I just wanted to add that I am assuming that the mini-mash is composed of both specialty grains and base malts. If not, then the specialty malts do not require any type of conversion and can basically just be steeped using the process I outlined above.