So you don't need to make a 700' run from the dish, you need to make a 700' run from the house to a single receiver in your man cave?
The error 47-137 is saying you have a weak NETWORK connection - i.e. the networking between Directv receivers. Judging from the picture you are trying to put a C61 client in that location. That is probably never going to work, it needs bidirectional communication over the coax (meaning no amplifier can be used) and is more sensitive to distance than extending satellite that far (and running it off that second splitter that's not designed for Directv usage is only making things worse)
However, since the C61 only needs network to operate there may be another, easier way to go. I'm guessing the man cave isn't connected to your home network now or you would have mentioned it. You can run networking over your 700' coax, just not the type of networking Directv uses.
Buy 2 of the coaxial network adapters, the 2 pack of DECAs, and the 8 port SWM splitter linked below. The setup you have now with a second splitter hanging off your 4 port SWM splitter is not ideal, especially when you're trying to do something 'non standard' like a 700' long run. Considering how little the proper 8 port splitter costs you might as well get everything set up correctly to make troubleshooting easier. So step 1 is to replace your 4 port SWM splitter with the 8 port.
Step 2, extend the 'house' end of that 700' coax inside, using a coupler or whatever. Run another coax inside that's connected to the 8 port splitter outside (so I think you should have five things plugged in that 8 port splitter, the 3 receivers in your house that currently are connected to the 4 port splitter, the 1 receiver in your garage connected to that 'other' splitter, and the 1 new coax you just ran.
Step 3, connect the coaxial ethernet adapters to either end of that 700' coax from inside your man cave to inside your house, then using ethernet cables connect them to the DECAs. The DECA in your house then connects to the new coax you just ran from your 8 port splitter to the inside, and the DECA in the man cave connects to the C61 in your man cave.
http://www.amazon.com/TRENDnet-Mid-Band-Transmission-Distances-TPA-311/dp/B00684E0UI
http://www.amazon.com/DIRECTV-Receiver-Ethernet-Adapter-Generation/dp/B00ZDUSPUY
http://www.amazon.com/Directv-8-Way-Wide-Band-Splitter/dp/B0045DVIP4