The Q150 has a 1500W night storage heater, and a 1300W boost for daytime use,and whilst you shouldn't need to run them together, you always need to protect the user. But that makes a total of 2800w, or 2.8kW, so is actually fine for a 13amp plug - not that I'd advocate that.
Most storage heaters have a dedicated consumer unit for the night storage circuit, but have the 1300w daytime boost wired into a 20a switched spur coming off the ring main circuit.
Whilst I couldn't recommend what the installer did, it was creative, and as 1500w is only 6/7amps, it was well within tolerance. I suspect that the first timer was faulty, and the replacement, just a cheap replacement that couldn't handle the current going through it.
As the installer badly screwed up, I suspect you may be able to get the job done properly (option 3) at a much reduced cost.
Am I misreading this?
I don't think anyone would use a 20 amp switch on a ring circuit WITHOUT some form of fusing down somewhere to 13 amp or less