Okay, so a number of issues here.
It is extremely poor form for a probation extension to come out of the blue. What is your company's probationary policy? Should you have been having regular objective-setting and review meetings? We do this every six weeks during the six month probationary period. The reasons given for the extension are completely stupid, how will you and your boss put an effective mediation plan in place? 'I will answer all emails on the day received'? - what are you meant to do if you have back-to-back meetings all day? I'm quite sure that, like any professional, you put your out of office on if you are in meetings all day, so that people know to text/call and leave a voicemail if it's urgent. So measuring email responsiveness would be daft. Should you open every meeting in the style of Robin Williams in Good Morning Vietnam to demonstrate you don't find it to be a hindrance??
What is the policy on home-working? We do not generally allow this for probationers (and indeed no-one can negotiate it as a formal right, it is always manager's discretion although it's very rare for it to be refused provided it doesn't interfere with the day-to-day operation of the office). Who was it who promised you home-working? What does that person say now?
What is the basis for you being supported by the consultant? I had this in my last job - he'd been brought in to cover the role whilst they looked to recruit as they were not expecting to find a candidate before the incumbent moved on. (As her entire handover to me consisted of the words "you know it, you'll be fine" this was just as well!). He was exceptionally useful to me in supporting me into the role, despite having much less experience of the particular organisation and area we were working in. So the freelancer is someone you should get on side, in my view.
I don't think you have any chance of getting severance whilst on probation, I'm sorry. But happy to be proven wrong by people currently working in the private sector (which I am not).
I utterly sympathise with you, by the way. But I wouldn't give up yet, even though it sounds crap. For a senior role, I think you should treat the probation extension as an opportunity (particularly because I suspect your boss wants you to see it as the opposite) and don't give the bastards the satisfaction of grinding you down.