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Hello. The common failure I see on these older cars for emissions is a slow or non functioning oxygen sensor.
I don't know what items are included in "the big service" but that is where I would start.
If that is Ok I have also seen fuel injectors in these cars get leaky and tend to drip fuel into the cylinders causing rich running.
Since I am sure it was tuned at the service that may still need to be checked for emissions compliance since they do run a bit better when rich but the emissions levels may not agree.
Hydrocarbons are unburned fuel, compared to Carbon Monoxide which is from rich mixture. So something is happening where fuel is not being burned or at least
Not burned completely.