is there any way to actually find the cable length...
As another person says there is the actual physical length of the wire, which is one thing. But electrically it may behave a little shorter or longer than that depending on what the wires are made of.
When the boost engineer arrives, they will have a rectangular blue box which a square LCD display on it, it is made by a company called JDSU, you will easily see the JDSU marking on it.
The JDSU can do a number of tests, you will probably find this is the first and only piece of test equipment they use.
The JDSU can do a test which will electrically show how ling the line is, it will also tell you how much attenuation there is on your phone line to the cabinet, ask the engineer and write down both of these numbers
The JDSU also typically, at least in and around the location where I live, connects to ADSL and VDSL at lower speeds than the modem you use.