He wants to transfer the money to me and wants me to buy the property all cash.

When purchasing a property that is occupied the lease transfers with the title, therefore you are required to honor the remaining duration of the lease. 

But actually the issues that I had were not operational issues, it was more administrative/red tape and I don't think an inspection would have caught it...

But how do people actually get the note recorded with the county remotely (making sure the mortgage and the note transfer to my name at the county level)? 

In terms of the Transfer inspection (locally called U&O but it is not actually a U&O inspection/cert) I find it to be very effective to have a local contractor be present for the inspection and I try to be there myself as well. 

You need a portable alarm system from simply safe.No hard wiring ,no drilling into walls,100 percent transferable from property to property,and they scare the heck out of squatters and thieves.You should also upgrade the door locks and window locks as well.Put alarm signs all over the front of a the property and their is a good chance no one will even approach the doors to try to break in.

Does anyone know how long it takes for the deed transfer to take affect?  

One option is to transfer more funds to the 401k form other IRAs or former employer plans. 

I have not bought from them because they didn't release tapes very often but have spoken with them several times at conferences.

I suggest you re-enlist and request a transfer to wherever you want to end your Military Career at.