Sorry, I assumed your box already had v13.0 since there was an over-air update broadcast a couple of years ago. The issue of stuttering on these boxes has always been somewhat of a mystery. I think the trouble is that there are multiple causes which have similar or the same stuttering symptoms. The v13.0 software was aimed at stuttering problems that happened overnight in some areas at DSO. By all means give it a shot though. If it doesn't work, you could try connecting the drive to your PC and try running Western Digital's Lifeguard diagnostic program on it to see if it detects any errors (if it does, then at least you will know the HDD has to go).
Trawling through past threads, somebody did try a 500Gb drive in a T825 (albeit it was a SATA drive via adaptor), and only 327Gb was used. So, a larger drive may be usable - just the extra capacity will not be used.
Of course, the cost of a new hard drive also has to be factored against the price of a new or refurbished PVR. For example, you can pick up refurbished T835 boxes for around £40 (e.g. Agora branded) which is essentially a more compact version of the T825, with less connectivity options. And that price probably isn't that different from buying a new HDD. New T835 boxes seem to have rocketed in price and are poor value for money these days, compared to the newer HD models where you can get a 1Tb T7650 (Logik branded from Currys) for £160 - again similar in operation to your Digihome. Argos do a 320Gb T7650 (Bush) for £150, but obviously the Currys price is better value.