I have had all the same fun and games you are describing with my 2000S. It turned out to be an MAF on the way out and a pair of oxygen sensors in a really bad way, one so bad that that bank was bringing up misfire codes. When I replaced both the MAF and O2 sensors it was back to normal.
On a side note, if your car has been doing this for some time you may want to check the catalysts for damage. I switched to bypass pipes when I replaced the sensors as it was a less expensive option than new cats. I am now catless, as in Australia we only have to run one set of cats so the Boxsters only have the main cats and one set of O2 sensors.
Good luck.
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