not going to work, sorry.
i am not being pessimistic, or trying to be negative; i am speaking from personal experience.
i have been into this hobby for 23 years and have put up at least 10 different CB antennas by myself in different locations. (those do not include antennas ive put up for others)
in one of my installations, i was putting an antron 99 on 30 feet of pole on the side of my house, very similar to your situation.
in my situation, instead of a chain link fence it was a cinder block wall.
the distances involved were almost exactly the same as yours. (distance from the side of the house to the fence/wall)
i put two guy wires into the cinder block wall, and two across the roof.
it lasted two months just fine, and i thought it would continue to work, until a particularly gusty day, (not more than 50mph) when i came home from work to find my antenna laying horizontally across my roof.
the mast had folded (1 1/4 inch tubing made for antenna masts).
the guy wires were still all intact. i got very lucky that nothing, including the antenna was damaged.
what was the culprit? the angle!
those two guy wires i put in the cinder block wall did not have enough of an angle to them to be effective.
you really dont want to go much less than a 45* angle coming off of the antenna mast.
much less than 30* (approx) and the guy wires dont really serve their purpose very well.
right now, as per your diagram, you only have two directions covered.
it wont make any difference whatsoever whether you mount the guy wires to the fence or the eaves of the house.
the angle is just not great enough.
have you considered mounting the antenna in the center of your roof?
this would give you four good guying points. one at each corner of the house.
if you can find a three foot tripod, it might be just the ticket.
i hope my experience can help you.
i cannot overemphasize the worry factor in a base antenna installation.
at the VERY least, you will have a broken antenna, and will likely be too discouraged to put up another one any time soon.
LC