As far as the overlap of your codes, I suspect not. OEM gas cap should be pretty cheap. First try that and see if evaporative code goes away. You might get lucky and after resetting the CEL, you might get only P0420 code back after few miles.
If the wiring does not look like chewed up by mice, you have to eliminate bad plugs or bad coils as the source.
Sometimes, the miss-fire code is triggered because your mixture is too lean. But generally, that results in P0171 and/or P0174 codes. On the off chance that the mixture is occasionally lean but not enough to throw lean code, clean your MAF using *only* approved MAF cleaner. CRC makes one in a red can. MAF's are delicate so handle it with care. If your MAF is dirty, this fix alone would make you amazed with the performance improvement.
If you still get the P1300, then you might have to look at the state of the spark plugs. If you are running anything BUT NGK, get the OEM NGK in there. If you have Bosch, then this will explain P1300. The dual laser platinum NGK (about $10~$12 each!!) lasts easily in excess of 100K miles. I have yet to hear about a dual laser platinum NGK which came off a car after 100K looking worn out i.e. they all looked as if they would go another 100K. If you are not the original owner, it is highly likely that somebody replaced those expensive plugs with a cheapo versions and you are getting P1300 code. In that case you will end up spending $60 on the plugs and wait to see if P1300 returns.
Once you are on the solitary P0420 (and/or P0430 I don't know if your engine has total of 3 or 4 O2 sensors) you start doing voodoo incantations to get rid of those codes
This is what a *good* mechanic will do.
- Vikas
P.S. And for God's sake, don't just disappear when this saga is over. 90% of these topics end up with NO resolution. The original poster never comes back to update the final outcome :-(