Have you done this journey before? The tube from LHR to St Pancras is possibly quicker and more reliable than the HEX and a taxi. The tube from Paddington to St Pancras is probably more reliable as well.
If your flight is scheduled to land at 9, you may not actually get off the plane until 9:20, add 20-60mins to get through non-UK/EU immigrations, meaning you may not even get the 10:12 HEX from T1/2/3, if you do you may not get in a taxi until 10:40, from there the journey can take anywhere from 15-30+ minutes depending on traffic, then get to the right platform/train.
All going well it is possible, but I wouldn't rely on it.
I've done it once before and it all worked out but more so likely due to good luck.
That being said looks like taking the tube to kings cross and walking across the street to st pancras is the way to go. You locals obviously know your stuff. I just remember accessing the tube was a pain from T3 and the damn tube train is so hot inside...ugh...
That being said I already bought my 23 quid HEX ticket so I'm locked in. Perhaps next time I'll follow the sound advice given here.