SOLVED!
I solved my 02/H02 problem myself. The bottom line is endlessly repeating the Ford Drive Cycle is not the solution - it's contributing to the problem.
To clarify - the issue is that in certain 13-14 Mustangs the 02 and H02 sensors refuse to "ready" for emissions evaluation. Without exception these cars have some exhaust mods ranging from H pipe/cat back, axle back, or like mine, just mufflers. No matter how many Ford Drive Cycles are performed the 02/h02 monitors wont ready.
SOLUTION: The problem seems to be the modified free flowing exhaust prevents the cats from getting hot enough - for long enough for the 02 and H02 tests to run. The Ford Drive Cycle contributes to this because it keeps the speeds between 40-65 MPH and thus the RPMs and load are too low to build and maintain sufficient cat temp.
Normal driving and the Ford Drive Cycle on my car produces cat temps (as measured via my nGague) typically between 650-1050-degrees Fahrenheit. From my tests on my car (bone stock 13 auto with Ford 13-14 GT500 mufflers) it appears minimum cat temps of 1250, and better 1350+, best 1400+, are necessary for 15 mins, followed by 15 mins of normal 40-65 mph driving (700-1100 cat temps) for the 02 and H02 tests to both start and complete.
I note the necessity of normal driving because it seems the cats need to get hot for the test to start then run at lower speeds for the test to complete and the 02 and H02 to show ready. In my tests they won't show ready until after the heated cats cool off in 10+ mins of normal driving.
On my car to get and maintain this cat temp (1325+) for 15+ mins this requires sustained 80+ mph for over 90+ minutes, or driving a warm car at 3k-4k rpm in 2nd or 3rd gear for 15 mins while monitoring cat temp and adjusting the throttle accordingly to keep the temp in range. I suspect this is not necessary for stock exhaust cars to ready because they have increased exhaust backpressure. Thus, if you have a more modified exhaust, such as a cat back, you may need greater rpms to get cat temp in the range I describe.
Note it takes some time and rpm to heat the cats up to the range and then slightly less rpm/throttle will keep them there but if rpm/throttle drops below 3k the cats can cool 300-500 degrees in just 15 seconds so consistency is vital. I don’t know what impact momentary dips below this range will have on the readiness process but these 02 and H02 sensors are sensitive little bitches so I recommend you strictly stay within range.
Also note though I list my rpms and gear it seems to me the real driver of cat temp is load. Cats will get hotter easier and faster driving up a long hill and conversely will be faster to cool with the same RPM going downhill. So really, I think monitoring cat temp while driving is a must to do this accurately and reliably. Otherwise, I guess you can just drive a warm car at 3500 rpm for 20 mins but that's kinda winging it.
How I came to this understanding is I went on a 4-hour drive and the 02 and H02 went ready after about 2 hours of steady 80+ mph. They did not go ready in the preceding 2-hour drive with traffic where my speed fluctuated between 40-80 mph. I was monitoring the cat temps and 02/H02 readiness the whole-time given recent conversations with a local tech and another tuner pointed to modded exhaust as the problem. After the drive I cleared the monitors and performed the high rpm/low gear drive the next day using cat temp as my guide. I kept them above 1350 and got the 02 and H02 to ready after about 10-15 minutes of high cat temp driving followed by 10 mins of normal driving.
I then cleared my monitors again and repeated with the same driving test with the same result in the same time. So, after repeating results 3 times I think it’s problem solved (God willing, knock on wood.)(I’m not taking any chances!)
It's been a long 2+ year siege to solve this f&%*ing problem. I've had the three-best local “Mustang guru” tuners look at the car, a Ford Service lead tech who was befuddled and consulted with Ford Corporate, and several experienced local mechanics look at the car with no consensus other than start throwing parts at it ranging from spark plugs and 02 sensors to the new cats and ECU. Only my last local mechanic, along with another tuner, both pointed to exhaust mods which gave me the clue cat temps may be the solution.
LUND racing, who I imagine must know of the importance of cat temps – at least if they’re as good as they advertise - would not take any time to help me despite that I'm their customer. Or maybe it was just above their knowledge/ skill set – I don’t know – but they could have at least tried to help.
Many forums have threads of this issue with frustrated owners like me but no solutions short of returning the engine and exhaust to 100% stock then it corrects itself. Problem is in states like NY the car must pass the test every year so returning the car back to stock yearly is a real burden.
Owners perform countless Ford Drive Cycles desperate solve the problem to no avail at the encouragement of people who insist the drive cycle is the solution when in fact sometimes it's not the solution as with my car. A few owners said they sold their car in frustration. I was considering this myself.
I hope this is truly the solution for everyone with this problem and this thread helps others in the future.
Thanks to everyone who commented.
Best regards and good luck!