Yeah - I agree with your analysis.
A good idea on your way forward - you will have to appeal to their better nature however. Because Mersey Travel is 'locally accountable' to the Liverpool City Region / local govt it may be worth you contacting your local councillor to ask them to support a request on your behalf - basically you need to get your Councillor to take it up as a case and ask them if they would be prepared to look again at the sum they are asking for and reduce it, esp if you have any mitigating circs eg - low wage, part time, student or some such - a Councillor should be used to making representations on behalf of constituents in this manner so no harm in asking.
Go on your local councils website and find the info that tell you how to contact Councillors by ward - most have a postcode finder that tells you how to contact them. Chances are that you have never heard of your local Councillor but they are often very happy to try to help constituents.
In practical terms best way to do that is to write to MerseyTravel with your request - then send a copy of that to your Councillor with a covering message asking them if they can help / support by raising the case on your behalf with MerseyTravel.
As they operate locally it's not unusual to maybe even ring your Councillor to discuss it and seek their input/advice/ help.
Good luck with it