AE round does stick a bit in barrel - seems to be slightly larger than other brands' ammo.
Bingo!
If the cartridge doesn't pass the "Plunk" test, it's not going to work well in use (if at all). It sounds like the overall length is too long on the AE ammo and it is causing your issues. 9mm CZ's have a short leade and thus cannot run all brands/types/shapes of ammunition. Head over here:
https://czfirearms.us/index.php?board=33.0 to get more information, specifically here:
https://czfirearms.us/index.php?topic=34225.0.
If you google "plunk test" there are plenty of videos explaining the process. It's very simple to do and should be done with any ammo before purchasing in bulk. Knowing the ammo passes the plunk test will alleviate many ammunition related headaches in CZ's.
Make sure you also pull your magazines apart and clean inside and out, leave dry and reassemble. A detail strip, clean, and lube on the firearm is also recommended. The grease that comes in the gun new is not a lubricant, it is a protectant and needs to be removed prior to use.
So fired another 105 rds which all cycled perfectly - 100 Magtech and 5 Federal HST. Ejection is almost perfect at 8-10' so believe extractor is good.
If the recoil spring is "perfect" for HST, it is most likely too strong for the plinking ammo. You might want to consider a recoil tuners pack from CGW. Once you settle on an ammunition favorite (that passes the plunk test and is accurate for your needs), you can tune the recoil spring for best operation. I run a 12lb spring in my SP-01 with target loads. I think the factory is either 14lb or 16lb.
Cheers,
Toby