If the injector for cylinder #1 is fixed. The dealer stating that cylinders #1 & #3 are down, would mean in my opinion that those cylinders are down on compression. If so, how much is the big deal.. Again, this is just my opinion, but I bet you have some piston damage, like I did... "ringland fractures" which allow the cylinder to leak down quickly when not running but when turned over to test compression. Mine was caused by me spraying denatured alcohol ( ran out of methanol) and lugging the engine which resulted in too much fuel/liquid in the cylinders and caused chunks of 2 pistons to break away and cracks in the ringland area of a 3rd. And if I'm right ( I truly hope I'm not) they will be tearing your engine apart next. Since you have a tune, and the dealer has sent Ford all the data, which includes all of the things they request in that TSB I mentioned elsewhere, Ford won't warranty anything that is even remotely tune related. If the non-Ford dealer burned thru that much fuel testing their theories, they may have caused the problem, or it may have been caused by the injector flooding the #1 cylinder. You can blame much of this on the #1 cyl. injector, but not sure how the #3 cylinder can be explained.
Also, I wasn't truthful at first, and believe that not admitting things makes the dealer less likely to be helpful. (The service writer directly accused me of tuning my car and I denied it.) My vehicle was completely stock when it went in, except for badges and the rear Magnaflows. Ford got pix of all of those mods plus my painted calipers, custom wheels etc. Ford told the dealer that the sent data proved my ECM had been flashed over 100 times ( close...) and that the last time was only 12 key turns ago... and vehicle had 35K... You may explain away a couple flashings to a dead battery... but not the number I had. If it's a major repair, that's about your only hope, and proof of the accident/towed vehicle that wouldn't run.
Good Luck!