To be fair to the council, from your post it does sound like you yourself made certain assumptions and omissions following finding a cover on the meter.
thinking that unlimited parking was allowed
I had not noticed the bays had been changed to disabled with a 4 hour limit
Also you admit you didn’t check the signage:
which is why I didn’t look for further signage
The ‘Blue Badge Rights and Responsibilities’ on Gov.uk does actualy state ‘ These are the parking concessions available to you as a Blue Badge holder. However, you must always check signs to see what the rules are when parking’
Also, if the meter had a cover on it, how can
The meter inferred a pay and display
Did you take photographs of how the covered meter inferred this?
To be honest, as you describe it, I can rather understand why the council rejected your appeal due to the omissions and assumptions on your part.
An option was to probably ask for some form of clemency/leniency by sending in a rather grovelling apology for example being a visitor to the area and not knowing what to do with the meter being covered etc. Also saying how hard a monetary fine will affect you financially.
Even to the extent of giving them some flattery (which council’s generally like) e.g. ‘I hope this matter can be dealt with mercifully and sympathetically, which is the renowned hallmark of Torbay Council’.
However putting in FOI requests which will ultimately cost them time and money may rather negate any form of clemency from the council!
However, you are, where you are. Following your failed appeal:
https://www.torbay.gov.uk/parking/appeal/
Your only option is now taking it to the Traffic Penalty Tribunal for England:
https://www.trafficpenaltytribunal.gov.uk/
However you will need a certain level of evidence to present your case to the tribunal having read through some of the past ‘Blue Badge’ decisions on their website:
https://www.keycases.info/contravention-types/parking/?issues=blue-badge