A couple of thoughts....
* First of all, I won't waste everybody's time asking questions the OP already answered or rambling on about unrelated gun types.
1. It is well reported that the Tisas clones had extractor problems in the first year or so of manufacture. It is also reported that Tisas was very responsive to feedback from the importer (LKCI) and made adjustments to the design. This apparently corrected the problem and the newer manufacture Regents have not had the same issues.
2. I personally have one of the newer guns and it has had no extraction issues. It has other issues (thumb safety does not prevent all sear movement), but does run reliably, has never followed, or otherwise mis-fired.
3. Bill Laughridge at Cylinder and Slide is one of the top BHP smiths and his crew knows what their doing. They are doing their own custom builds on the Regent frame, which says a lot. Award winning pistol smiths don't risk their reputation by putting out high dollar custom gun builds on a chassis that has fatal flaws.
4. A careful read of the C & S site will reveal that the extractor cut in the BR9 slide is cut narrow "If you are ordering an extractor for a Tisas BR9, please put Tisas in the "Pistol type" field when you check out. The reason being is the Tisas extractor cut in the slide is narrower than Browning, so a thinner extractor is required."
5. I recommend putting a caliper on the OEM extractor and then the BHSS one and carefully note the difference.
6. Then measure the slot in the frame that houses the extractor. This would best be done with gage blocks or feeler gages, but absent these, you should be able to get a pretty decent measurement with the ID tips of your caliper.
physics and mechanics are what they are....either...
a.) the chamber is cut too tight and there's no extractor improvement that can yank the case.
b.) the extractor hook geometry is off and there isn't enough positive engagement to yank the case, or the contact face is sloped and the force is pushing the hook off the rim.
c.) the extractor is binding in it's slot and is not rotating into position fast enough for the hook to get a good grip on the case rim.
d.) the extractor spring is weak and not able to rotate the extractor into position fast enough.
Based on the OPs fluff and buff and report that fired cases slide out easily, I suspect (a) is not the problem... but one would have to check the chamber with a gauge to know for sure.
Based on the OP having just replaced the extractor spring I think we can take (d) off the table.
I'd be very interested to see what the BHSS extractor looks like, measures in thickness, and where/how much filing was done on it.