How do I replace a strip light with wiring that doesn't match the old light?
If I understand this situation correctly, both red cables are Positive and carry the current from switches. You may want to check both red cables if they really correspond to these 2 switches. If so, I guess You need to choose which circuit (1st red + N + E or 2nd red + N + E) You want to use, cuz I guess You will be using just 1 switch/dimmer (as Your 'new' light needs only 1 Positive cable).
I would check (for safety meanings) red cables (if both run current while switch/dimmer is on), put 1 red to 'A', 1 negative to 'N', 1 earth to 'E' and ISOLATE remaining red cable (using some isolation tape or else). If everything goes well, 1 switch will turn Your 'new' light up and remaining switch would be obsolete.
I'm not sure about all the fixing (if it needs to be done by qualified worker), but I did something like that several times myself.