So what am I supposed to carry around on a day to day basis?
There are two seperate issues here -
1) being able to identify yourself if requested to do so by for instance the police, the Straz Graniczna, Sluzba Celna, etc - in this case, an EU/EEA/CH driving licence is enough. They might want to clarify it, so carrying around a photocopy of the permanent residence certificate will be more than enough to satisfy them.
If they get really arsey, they could demand an ID card or passport, but in this case, the permanent residence certificate wouldn't satisfy them anyway. The only time that they would expect to see the national ID would be if you're stopped crossing a Schengen border - Schengen law says that you must carry national ID when doing so, and again, the permanent residence certificate wouldn't be enough to satisfy them.
2) Being able to identify yourself when a dowod osobisty is requested, such as at the bank, the Urzad Miasta, etc - in this case, you need to have a national ID, which is either a passport or national ID card - again, the permanent residence certificate isn't a national ID and shouldn't be accepted.
What nationality are you?
Incidentally, anyone refusing credit for stupid reasons like you list above should be ignored anyway - who wants to deal with outdated thinking?
But...if you want something convenient, couldn't you just obtain Polish citizenship if you're married to a Pole and have been here for over 5 years? It's certainly the easiest way!