Contacting them on social media can be a useful way of getting their response in writing, which avoids having to SAR them for the recording of the phone call.
As you'll probably appreciate, when a passenger is delayed by over 60 minutes and the delay is longer than it would otherwise be because of a TOC restriction on the ticket, TOCs in Britain tend not to comply with their PRO obligation to re-route passengers at the earliest opportunity on another TOC, unless of course general ticket acceptance is arranged with that other TOC.
If ticket acceptance is arranged, fine. If ticket acceptance is not arranged, the purpose of contacting the TOC is mainly to establish that you asked them to re-route you at the earliest opportunity and they refused, which is an important piece of evidence to have in your possession before incurring extra costs in re-routing yourself.
I wouldn't suggest travelling on a ticket that is invalid because of a TOC restriction and then trying to argue against, or seek reimbursement of, a penalty fare or Anytime fare charged on board. Instead, I would suggest asking the relevant TOC to re-route you at the earliest opportunity and then, once you have evidence that they refused, re-route yourself by buying the cheapest available walk-up or last-minute Advance ticket. The idea of this is to be able to demonstrate you took reasonable steps to minimise any out-of-pocket expenses you incurred because of their failure to re-route you. Also, do not request a refund on the original ticket, because then you'd have chosen option (a) - a refund, and would not therefore be entitled to option (b) - rerouting at the earliest opportunity.
If the cheapest available ticket for re-routing purposes is a walk-up fare, there is an argument for boarding and then seeking out the guard and asking permission to travel on your existing TOC-restricted ticket. The advantage of this is you might get a guard who will just let you off (on a discretionary basis rather than because they're correctly applying PRO, but the result is the same), and if they don't let you off they'd probably be willing sell you the cheapest available ticket (i.e. off-peak where valid, with a Railcard discount if you're entitled to one) if you approached them and explained the situation.
But the risk is you may end up paying a premium because you boarded without a valid ticket, and then when you try to claim the money back you're vulnerable to the allegation that your claim is for more than the costs you should reasonably have incurred in the circumstances. If you board without buying a new ticket and just sit down, it could also look like you were hoping not to be checked and thus travelling without a valid ticket hoping to avoid detection, which is not something PRO entitles passengers to do, even if another TOC has failed to abide by its PRO obligations.