That's what I thought you were going to have to do. (Go to underneath the slide)
I gave it some thought for a bit, because I was going to do it until I found out it was $10/mth to add an extra receiver.
You need to get the wire into the space behind the basement storage wall then you have a few options to get it to the bottom of the slide.
I was going to go down the stink pipe vent and mount the antenna on top of the vent cap.
Taking the back wall down in the basement I could see the vent stack pipe in my rig and was going to drill a small hole in it, then fish a fish tape up through the hole and out the top. Then seal up the hole.
If you think that idea "stinks" then....
With the amazing 360 view of you trailer on the Jayco site I can see your fan vent in the kitchen is fairly close to the wall.
You should be able to stick your arm through the truss space (in the middle of the picture) to the top of the wall. I'm pretty sure that's where your wire for the fan's wall control is going to come out and there will be a hole drilled large enough for them to get the RJ11 connector through.
If you want to do the antenna mounting inside the fan, like mentioned, or pass the with through the side edge of the fan to the roof, like mentioned, you could maybe fish the wire down that hole in the top of the wall into the wall and make your way to the basement through holes in the closets.
Here's a picture of where you would have to stick your arm. I was able to stick my long skinny arm in there, but if you have Popeye forearms you might not get in.