I have no direct experience with the 7962, but have deployed dozens of 7960 phones and have never run into this. I know the 7962 uses XML-based configuration files, but that’s about it as far as differences. The SIP firmware for these phones is far from impressive IMO.
While I haven’t run into your specific issue, I have encountered a few other small annoyances. From another user on here, I learned about a project that implements the SCCP protocol as an add-on for FreePBX. I wouldn’t call it a finished product - there are typos, missing help, etc - but from a purely functionality standpoint, it certainly allows you to interface Cisco phones using their native skinny protocol with FreePBX. (Frankly, this module was more like what I expected when I bought the third party phone support.) My plan is to deploy a few extensions using this module after other projects calm down a bit here and then evaluate how it works compared to the having the phones flashed to SIP.
Don’t know if you want to consider using it or not, or even if it’ll help solve your problem, but wanted to provide you the information. A link to the thread I posted with a bunch of info on this module is below.
Best of luck!