Will Comcast Replace the Drop Line?

I have a 600 mbps plan and have been getting around 210 average at this new address. The house was built in 1975 and I have no idea how old the cables are in this neighborhood. The drop line comes out of a steel conduit in the backyard and then connnects to a booster on the OUTSIDE of the house. Having the booster externally is already not an ideal situation but it does look newer and in good repair. I recently had to move my modem to a different jack as the one line I was using had constant connection drops. The line it is on now is stable but my speed is severly lacking. I imagine the lines coming off the booster were installed at the same time as the drop line to the house. So if the lines throughout the house have degraded I have no reason to believe the drop line is not in the same or worse condition. 

The 210 mbps average I am seeing is on a wired connection. On wifi I can see anywhere from 40-170 at any given time. I have C7000 Nighthawk which is capable of 1 Gig, so my modem is not a limiting factor. I also plugged directly into the drop line bypassing the booster and the entire house network of coax and saw the same 210 speed average. So while the wires in the house could likely stand to be replaced at this point, they are not responsible for my speed limitation.

Will Comcast replace the drop line to my house and how long does it usually take to convince them to do that? I already know I am going to have to play the song an dance of tech support that will make me restart my modem 100 times before they will commit to sending a tech out to speed test the drop line. Just curious what my options are and how hard I am going to have to fight to get my speed to where it should be.