Decide which Motorola STB or DVR you want to use for the tv signal to the Slingbox. Place the Slingbox in that location and connect via component cables and L/R audio cables from the Motorola STB or DVR to the Slingbox. Plug the IR remote wire into the Slingbox and place the sensors on the front top and bottom of the Motorola STB or DVR. Now, you need to get the signal from the Slingbox to the U-Verse RG located in your garage. You need a wired solution for that. Unless there is another wire in your house for that, you will need a SlingLink Turbo. Plug one unit of the SlingLink Turbo into your Slingbox and an empty wall electrical outlet. Plug the other SlingLink Turbo into your U-Verse RG and an empty wall electrical circuit. I don't know why you would balk at the SlingLink Turbo. It's inexpensive and works.
Now, all that said, if your Motorola STB or DVR has an ethernet port, it's possible you could plug the Slingbox into that ethernet port to send the signal back to the U-Verse RG. I am doing that with my Roku, but I have a U-Verse Cisco IPN-4320 DVR. I don't know if the Motorola box has the ethernet port and if it's active. Give it a try.