I almost exclusively book advance purchase train tickets, which in my case leave from Liverpool Street - so a very similar travelling time from Heathrow. I also don’t need to be at the station more than a few minutes before the train departs, unlike the OP. In my case, to replace a missed train booking on the day would probably more than double the cost, even taking account of transferring part of the value, and that would be to travel in standard class rather than First.

My personal risk is generally - where possible - to allow around four hours between scheduled arrival at LHR and the time I need to be at the station - 30 minutes to get off the plane and through Heathrow assuming a T5C, T3 with one of the more remote gates or T2B arrival, then 90 minutes to the platform at Liverpool Street, allowing me about 90 minutes of flight delay before I really have a problem and need to pay out for the Heathrow Express. The very least I’d consider is 2.5 hours.

The OP will most likely arrive at T2B with AC, with an immediate 15 minute walk to get to the main terminal, so I’d be allowing at least 60 minutes to clear the airport, and with greater immigration unpredictability more likely 90. Tube trains are more frequent than from T5, so it ought to be possible to be at St Pancras, having walked through from King’s Cross, in about 80 minutes.

So, that’s 2h50 minutes gone even with an on-time landing. If the need is to arrive by 1:15pm, that really does not allow much margin for flight delays.

Unless the OP has a very high tolerance of risk at the very least he or she should be planning to pay for the Heathrow Express - assuming it’s running.