Primer- Zinniser oil base alkyd
Paint- Benjamin Moore oil based alkyd (off white)
Method- HVLP at 30 psi
I don't know if that helps. My background is commercial aircraft painting back in the late 90's (Enron). But I have to admit I'm not super knowledgable about other paints and applications (I'm kinda a one trick pony in that regard) and I haven't painted much since, just a few off road rigs here and there for friends.
I have been away from doing painting as a pro for about three years, but did it for 17 years before that, and products change all the time. My line of work was residential and commercial painting and cabinet finishing with a few personal auto paint projects thrown in. It was common for us to spray cabinets with oil, but about 10 years ago, I switched to doing mostly commercial work and didn't do cabinets very often. It got to where oil based paint was not worth using or wasn't available in a good product. Behr became my go to paint and their water based product worked as well or better than anything else I used and it was available all over SoCal and until 10pm at HD. I did many other trades and was at HD all the time anyway. Painters have their preferred brands and some may have been better, but our customers liked the lowest bid and were thrilled with my work. I used some $50 per gallon SW interior water based paint for a restaurant, 10 years ago, and saw no benefit. Needless to say, I wasn't in the habit of trying all the expensive products to find a high end finish.
I love zinsser cover stain, both in oil (that was all we had for quite a while) and in water based. It sticks to glossy surfaces and kilz claims to require sanding or deglossing first. 123 and BIN (shellac based and thinned with alcohol) were also very good.
Without looking at the paint label ( I didn't use much BM) it appears to be solvent based. If it says to clean with paint thinner, it is solvent based.
I have a really nice binks 2.5 gallon HVLP pot setup, but used mostly Binks conventional 2001 guns.
If the paint got thicker when you mixed it, that is the problem and it won't matter how you spray it. I always use home depot for thinner, unless I am using an auto paint, and the paint thinner I have had around the garage has worked fine for thinning oil based cover stain and rustoleum oil based paint. That can has been around for about a year as well. The new lacquer thinner I got at lowes last week, had a different label and the HD paint thinner seems to have had a few changes to the label in the last few years.
I do not know if the thinner formula has changed much, or if the labeling/wording has just changed to meet AQMD/EPA rules. Some of it says for cleaning, but not thinning. If you add it to paint/primer, the VOC's go up and the "authorities" have a problem with it.
I know a guy who owned a paint company in SoCal and dealt with all this and knew the chemical side and political/business side, but I have not seen him in person to ask him about it.
Like others said, abandon the batch that got thick. Try some straight paint, if you have any left, with a different thinner if need be. I have not had paint get thicker when adding thinner. Who knows what would happen with the wrong solvent though.
That breakthrough paint sounds cool. You need it thin enough to atomize and flow, but not run, and you want it to dry fast enough to keep stray particles out of it without it flashing or doing anything else bad from too fast of a dry time. With your past experience, it will probably be smooth sailing once you get a material that is working properly.
The hybrid oil that cleaned up with water (devoe and glidden had them) was thick and it dragged like you were trying to brush honey. It dried way too fast to get nice results from brushing and rolling. The worked looked OK but it was a paint to use. It stayed tacky for a long time and felt like duct tape adhesive and it had an odd scent to it.
I don't remember if you figured out what your paint needed for cleaning and thinning, but try mixing a small amount of straight paint with some water and try the thinners on hand, and see what happens.
Talk to the BM store about the paint. They should be able to help you out. I tried some of the devoe hybrid and didn't like it and ICI paints made it right for me, but I was a regular in there at the time.
I am assuming you mixed the paint well before trying to thin and you used a clean container, since you have experience. That thinner may be junk.
BM has water borne oil based alkyd paints that they claim have all the properties of oil but clean up with soap and water. Do you have a pic, full name, or model number for that product?
. If it were me, I would trash the paint that's been watered down. If it were thickening up as you mixed it, it could have had a reaction to the thinner. I seem to recall something like that happening to me back in my early days of painting but I don't remember what caused it.