My point is the native res of the print Epson driver is 360 so if you stick to integers of 360 you'll be OK as long as you don't go below 180 to avoid pixelation.
You can certainly print below 180 without pixelation depending on the image and the substrate. Yes, you need to be careful, but really 120 is the point at which you really need to be concerned in most cases. Obviously it won't be suitable for some work, but you can certainly get down that far very often.
Native Image Res;
The two files are camera RAW files opening in Adobe Camera RAW.
The first one was set to 360PPI then opening in photoshop for printing.
The second image was set to 300PPI and then opened and printed on the same sheet.
OK, so they were both printed to the same physical size? That doesn't tell me if either of them is the native resolution in print. If the image is 3000x2000 pixels and you printed it on an A4 with a border you might have printed it at say 11"x7 1/3" then it's printing natively at about 272, so at either 360 or 300, it's being interpolated by Photoshop before being printed, which isn't the query.
The query is whether upressing or down sampling to 360 is better than printing it without any resampling.
Now it's entirely possible (likely!) that one your resses was native for the size being printed, but you haven't confirmed which. At the size printed, was it 300 native and you upressed to 360? That's valid. If both were simply opened at 360 and 300 respectively and then printed without resizing then they would print to different sizes and you're not answering the question at hand, which is if you want a particular size should you resample to 360 or go with what you have?
The file was printed at 720x1440DPI, but it doesn't matter which DPI you set as long as it's not a draft mode (you might even see it at a draft mode).
Mode was Finest Detail Off, High Speed On.
It does matter. It absolutely affects the dot pattern being laid down and that can affect the output. It's absolutely valid to test at 720x1440 is that's the resolution you want to use, but it's not the most common resolution to choose on an Epson Pro printer, so it's worth checking against other options.
To scan in I used an integer of the scanners native res, which was 96PPI to capture the effect. The scan is off a single sheet, no trickery.
I would recommend only scanning at the scanner's native physical resolution in order to avoid any errors being introduced. I wasn't for a moment suggesting any attempt at trickery! 96ppi is really too low. imho.
I don't think we going in circles. You have valid points and a worthwhile test to pursue, but there are things that either need to be confirmed or explained or, perhaps changed in order to validate it.
As Neil said, you can make a test to obtain any result that you want. If I have time tomorrow at work, I'll find an image and print it at various "native" resolutions and then at corresponding resampled resolutions - to be honest it may take a day or two depending on how busy I am. I like your approach of showing some actual examples for people.