Try these guys
http://www.x-sim.me/index.php?menu=home
8 hours precisely and $35 later and my device is free
I understand that you said you have evidence and that you spent money to free your device but Verizon iPhones are 100% Factory Unlocked -- I can confirm this also long with 100's of other members on this thread....
The report you have will say "False" thats normal, Verizon cannot lock the devices by law due to their agreement with FCC -- however they can have Apple report the devices as Locked...these phones otherwise would just have a the activation policy as "Retail Unlocked".
I think you can understand when you ask store reps (Apple or Verizon) they will never confirm to you that the Verizon iPhone is unlocked by default....its part of the Verizon agreement with Apple and we all know that every carrier likes to "lock" its devices so that customers don't flee to competitors.
Knowing their device is locked, customers will think twice about the possible extra cost to switch over...
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It's funny, my Verizon iPad can produce ATT LTE with the ATT sim. But if I put the same ATT sim inside my Verizon iPhone 5S, I only get 4G. No LTE even though I'm in the coverage area. Are the ATT iPad sims lock to prevent LTE on other devices?
You mentioned iPad, but dint mention what model?
iPad Air / Retina Mini = Universal, they support CDMA+GSM(3G/4G)+LTE on all USA networks without exception...something I have personally tested with both of those models.
Verizon iPhone 5S = 100% AT&T + T-Mobile LTE -- I am using it at the moment.
Why it doesn't work for you, be beyond me.