While I think this is the way it’s going to go as well, I think you are being a bit too hopeful on the price.
I think the PL would charge a minimum of £30-40 a month for their own service.
I really don't think I am. It would be counter productive for them to price it that high. According to that video Sky have around 6m football subscribers and BT approx 2m - even assuming only half of those that sub to BT also sub to Sky, you've got just 7m households in the UK that are paying for PL football. If the PL tried to charge the same prices as Sky are charging now then they wouldn't even get the 6m subs Sky are getting because of all the added value and convenience Sky offer, let alone increase the number of subscribers.
We're not allowed to discuss it in detail but we know just from reading this forum during matches that a large number of supporters watch PL games via illegal methods and some of them are likely to be paying £5-10 per month to do so. If these people could watch PL football on a legal and reliable service for £10-15 per month then they would and you'd see a huge increase in subscribers that will more than make up for the lower subscription fee. You have to remember that this wouldn't be a UK only offering too. While there's supporters in the UK that would pay £40 per month, you're not going to have a significant number of supporters outside the UK that will and it's these people that will make up the bulk of the total number of subscribers.
Similar to the point I made about Amazon yesterday, there's even an arguement for the PL accepting less revenue to increase subscriber numbers. I'm sure if you offered PL clubs 200m subs at £10 per month (£24bn) or 110m subs at £20 per month (£26.4bn), they'd take the 200m subs because those extra 90m households viewing will increase the value of both advertisement on the channel but also individual commercial deals each club will sign.