Ok, so I finally have an update on the moon clip issue...
I ordered 100 new moon clips from The Revolver Supply Company the week before leaving for vacation. Ordered on Friday, and they shipped on Monday with a tracking number that showed they were to be delivered on Thursday, which was perfect because I was planning to leave on Saturday. Well, Thursday can and went, and the USPS tracking showed them never moving past the origin sorting facility. I waited until the mail ran on Saturday, and NADA!. :-(
Well, at least I had also ordered the Rimz and had them shipped to my vacation address just in case.
On a more positive note, the BMT moon clip loader tool did arrive before I left. I tried it on some of the Old Sarge's clips just to see how it worked, and I was IMPRESSED! Very handy tool and well worth the money to me.
Ok, so after arriving at my vacation location I contacted TRSC
Moon Clips, These are the full moon clips sold by The Revolver Supply Company via email and asked them to check into the shipping status of the clips I had ordered from them. I requested that if they decided to reship, that they ship the new batch to my vacation location. Even though I sent the email after they had closed I received a reply, after hours, that they would check into it. Then, the next morning I received another email from them saying that they had shipped another 100 clips to me where I am, and just requested that I return the first ones if they were to show up.

I like doing business with companies like that!
I received the new clips a few days later and finally had a chance to get to the range today. I only opened and used one pack of 10 of the .45 moon clips from The Revolver Supply Company, but I did run a bit over 100 rounds through my new 625-3, using the new clips. I'm very pleased to say that with these new 0.040" clips the gun ran perfectly!
I also did fire a few using the Rimz. While they worked perfectly too, and were easy to load by hand (seem to be a good product), the BMT loading tool worked so easily and quickly that it was easier and quicker to just use the steel clips.
As a side note to my experience with my new 625, I tried a few rounds without clips just to test for function. Again, all worked perfectly!

No misfires or any other issues. I was also pleasantly surprised to find that even without clips, the spent cases were easily removed, even with the +P's. Some of them would just fall free and the rest could easily be plucked out with just the flick of a short fingernail.
So, in the end, as I suspected, it was just a matter of getting the correct thickness clips, and 0.040" seems to be correct, for my gun at least. I also can't recommend TRSC enough. The clips appear to be of very good quality and the way they handled the shipping issue, even though it was purely a USPS mistake and not their fault, says a lot about them to me. They shipped the original order immediately, responded to my emails after hours, and then shipped the second order just as fast, no questions asked. Good people!
And as we all know, every good thread requires at least one gratuitous picute. Here's a shot I took at the range today, of the gun in question with its new Ahrends cordia Retro Bananas, and the BMT loading tool.