Remove the post from your pop rivet.  Ream out the inside slowly until it is a press fit on your TS9 connector.  I used a drill press with a small drill bit to do this.

Cut off the RG-59 connector just behind the nut.  Sand to clean it up if desired.

Cut off a short section of RG-59 cable.  Strip both ends so you are left with the center conductor, an inch of exposed wire on one end, and 3/8in on the other.  Rotate it between your fingers and sand down the remaining foam insulation so it is a press fit in your pop rivet.  Keep the wire centered.  This took me 2 tries to get right. 

Sand down the wire end so it's about 1/2 the original width.  Round off the end slightly.  Test fit it into your TS9 connector.  DO NOT FORCE IT.  

Remove the foam from the wire, and press it into the rivet until it is about 1 diameter of the rivet from the end.  Trim the extra foam from the back of the rivet.

Push the wire back into the foam, which will now be a snug fit, until it is even with the end of the rivet.

Measure out the remaining wire against your F union and cut it off about 1/4 inch shorter than the rear of your union.  The extra length keeps the wire from pushing back into the connector when you push it onto your TS9.

Put your rivet inside your trimmed RG-59 connector, put the wire into the center of the F union, and tighten.  The rivet having a rounded back end seems to center itself nicely when you do this.

Plug it in, and use it.  Be aware that the force you can apply to the connector via this direct connection is much greater than the TS9 was designed to handle.  Use care and don't allow the spring tension of the mating RG-6 to apply any force to it, or you will be replacing your expensive mifi.