There's a big difference between accuracy and precision. Here are a couple of links:
NC State University ;
Wikipedia.
From the OP:
"[cycle computer] is repeatable and comparable results over a regular route (my commute which never changes) to within 0.5%" So we know that the cycle computer is precise. It gives reliably repeatable results.
From the OP:
"[GPS] distances are consistently recorded around 2.5-3.0% lower". The key word is consistently. We know that the GPS is also precise. It gives reliably repeatable results to within about 0.5%.
So, we know that both methods are precise to within ~0.5%. But we don't know if either is accurate. For that we'd need a gold standard reference measurement. And we'd have to ask all kinds of philosophical questions about what we mean by distance and crucially
why we need such accuracy, and exactly
how much accuracy do we need for that purpose. And that would get very boring.
It's certainly not justifiable to say that the GPS has a
"piss-poor" is inaccuracy of 2.5%. It could be that the holy grail reference measurement would lie slap between the two, in which case both would have a systematic inaccuracy of ~1.25%. It could be that the GPS is bang on and the computer has a systematic inaccuracy of 2.5%. How would you go about getting your reference measurement? Surveyor's chains? They will have a systematic inaccuracy too.
As we don't have a reference measurement, the best thing to do is
pick one measurement system and stick with it.
This problem gets worse the more complex the measurement system is, and the more more likely it is to contain systematic bias. This is why we end up having this discussion more often about elevation and derived measures like "moving speed" and calories burned than about distance. But the principle is the same.
Pick one system and stick with it. What's the worst that could happen?