Welcome to the community forum and thanks for your post!
Sorry that you haven't been given what you originally signed up for and for the promised call backs that never happened. That's not good
Don't worry, we'll pick this up and get you sorted. Click on my username and under the "about me" section you'll see the link to get in touch.
I actually have the exact same issue.
I signed up as a new customer on 29th July with Infinity and BT TV and Sport and added the HD Extra Bolton and it said if I took BT Sport it would also come with BT Sport HD. I have Eurosport HD ok but BT Sport HD and ESPN HD are missing. They are in the EPG ok but when I attempt to view I am told I need to subscribe and this will cost £4 per month. Even today the BT site says that HD Extra comes with BT Sport HD.
I opened another thread re this issue but hope you don't mind me piggy backing on this one as it shows I am not alone.
Tried to get it sorted via online chat, got through but the fella said he was from billing and had to put me through to a different q BT Sport Tech support chat but I gave up waitng after 10 mins in the online chat q.
As you only had an invitation to contact the mods posted to the thread yesterday evening -I doubt whether by that (mod controlled) method they advise to provide you with a telephone call yesterday.
Also when taking up the mods invitation - if you look at the invitation they advise how to do so. If you sent a PM as you posted that is not the way. Best make sure you have given them the relevant details correctly.