Are there any professional trainers that teach this method? What does one do if the slide doesn't go forward as expected on a reload?

I don't think so but I think we have two camps here and nobody is going to agree. I have certainly shared my feelings on the matter. The core question here is, is the OPs gun defective? The answer to that clearly depends on who you ask. So I guess the final answer to the OPs question is maybe, maybe not.

It should not do it , the slide lock locks it open insert mag reach over, release slide second nature . if it slams shut with the new mag and you like that well ok. None of mine do it M/P 9 LE sku 151215 black PVD .and new 2.0 in 45, Shield 9

+1

Not saying it's right, but it happens a lot. Saw a dude at my lgs close the slide on a brand new P320 X5 by inserting a new mag. Did it 3 times in a row, almost like it was a feature or something.

On mine it would happen if your grandma inserted the mag.  OK, maybe not that bad but it didn't take much.  Just going quickly will do it.  I had to TRY to NOT do it.  

I personally didn't really like it.  None of my other Autos I've ever had have done it.  Actually I have to remember if my G19 did it.  I don't think it did.  And I don't think my G26 does it either.  It must not because I don't recall it happening.

I KNOW it's never happened with any 1911 I've fired, any M9, not my XD 45 tactical, not my Savage 1907, or my HiPower.  Not on my Taurus 92 AS.  For me, it was just that one gun.  

So, I think it's something that should be deliberate.  In my mind.

I was reading one of these threads once and went and tried it with my Glock 17 and finally got it to happen on the third try. The amount of force I had to use was ridiculous, though.

my glocks do it. i like it. it has come in handy in comps. it jusr happens and i like "thanks im in a hurry"