Not sure why you would locate modem only 10 feet from base of antenna...
When we bought the house, we placed the combo modem/wireless router in the same place the old owner had one. The cable company used the first tap on the first splitter for the Internet cable run. The second tap feeds all the TV's in the house through a filter. I believe it's called a back-feed filter. (I have three additional splitters off the second feed, too.) Never had any issues until the change.
When I put the tower in, I found it convenient to place it near the shack. The inverted-L's were an afterthought.
To answer another question...the modem power supply is built into the box. Yup, first one I've seen without a wall-wart. The router has one, but it's quiet. But, a switching power supply could be inside the box.