Steve, I'm so sorry your Dad and family are facing this. A recurrence is so scary. I think you are doing the right thing in going for treatment privately. These things move so fast that we just can not wait.
I'm thinking that the chemo will at least buy time while you wait to hear back from John Hopkins. I would keep ringing them to push your Fathers case. You really do have to advocate strongly. I think that you are doing all that you can and should be very proud of yourself, I'm sure your Dad is.
Tammy

Caregiver/advocate to Husband Kris age 59@ diagnosis
DX Dec '10 SCC BOT T4aN2bM0 HPV+ve.Cisplatin x3 35 IMRT.
PET 6/11 clear.
R) level 2-4 neck dissection 8/1/11 to remove residual node - necrotic with NED
Feb '12 Ca back.. 3/8/12 total glossectomy/laryngectomy/bilat neck dissection/partial pharyngectomy etc. clear margins. All nodes negative for disease. PEG in.
March 2017 - 5 years disease free. Woohoo!