You did good.
I tend to agree with about 95% certainty. We have not eliminated a short within the t-stat wiring or the wiring to the AC unit.
I am trying to think of other scenereos that may cause your issue. Fresh batteries in the stat? I would not expect this to be the case, but if the AC system had it's own transformer and it was connected like you have it, it MAY be possible for the 24 VAC to drop to zero. Two transformers in parallel.
We never did determine if the stat was a heat pump/regular stat. The furnace definitely looks conventional.
So, I would suggest to remove and label all of the wiring going to the thermostat at the furnace (that will leave two wires going to the AC outside) and repeat the R to Y and R to G test.
Another odd ball suggestion is if there are any EXTRA wires in the AC unit, change briefly to another two running outside. Really doubt a problem exists here.
I'm trying to 100% eliminate everything else. I don't know if you own a multimeter?
Aside:
Note the automotive type fuse in the upper left hand corner. This is the fuse to the thermostat 24 VAC secondary.
Note the yellow an the Blue wire. Blue "probably" connects to one end of the fuse and then to R. Verify!
That would make the Yellow fat wire, the Common terminal on the stat. For future reference a Piggyback spade connector would be a way to add a common terminal should you decide to replace the stat.
The furnace boards DO NOT have to look the same. Some actually come with various harnesses to allow them to work with other models. This is just one example listing:
Honeywell Fan Control Board ST9160B1050 ST9160B 1050 | eBay
TIP:
If you do not have a hole house surge suppressor, I would consider investing in a wired in suppressor just for the furnace. Most furnaces have nothing in there for protection against spikes and RFI.
If you can't afford that, I would add a TVS on the 24 V secondary side. For about $5.00.
I HAD to add a $80.00 RFI filter on a carrier furnace because it was interfering with my power line automation controls.
I do live in an area where power problems are very rare including outages. The two important things, the computer network and the phone/answering machine and a PERS alarm are on a UPS. One repeater on my network is not. That power supply got knocked out at the same time a neighbor's oven controller was knocked out.
The importance of a commercial product is not the cost, but the warranty, Some have a $50,000 to $100,000 insurance policy on connected equipment and offer a lifetime warranty.
I am not 100% convinced. Maybe 95%, but not 100. Why, one side of the 24 VAC is usually grounded.
One commercial AC guy actually ordered a ceiling heat pump because he thought it was bad. When all of the effort to install the HP including overtime, it still would not work.
He asked me for some help. In about 10 minutes, working together, I said you have a bad t-stat wire and left him. Turned out the wire had shorted at a metal stud during a remodel.
In another instance, the installer didn't pay attention to the way the outside unit was wired. Two wires were paralleled and he paralleled the wrong ones. To make matters even worse for trouble shooting, the installed spliced the wires about 2 feet from the AC unit and then used different colors. The splice was crappy too without a drip leg. Using the wrong colors was definitely bad. It was a really tough problem to find.