Cable length vs obstructions
Your observation seems correct  but choice of cable is poor.  Except doors are dry wood and that makes a big difference.

Use SAT or CATV coax with satellite dish but LNA removed but located above chimney.

You need a high gain direction rooftop antenna in order to act as a passive repeater to be much stronger than the direct phone signal levels, otherwise, it will be worse by adding another multipath fading error.  

Old cheap sat. DTV dishes were only  5dB gain. Bigger ones , more precise ($) could get more dB gain. But this shows the ideal diversity ( beamwidth) vs antenna gain tradeoff.  A whip is almost isotropic but not down the end of the conductor, so close to 1dB gain.  It assumes direct line of site, so the miles is theoretical.









simulate this circuit &ndash; Schematic created using CircuitLab

This is like an ascii drawing of a house, ideal antenna aimed at tower above trees, with moot point about 75 vs 50 ohms considering coupling impedance between phone and whip antenna. SO I suggest you will need to wrap a few turns of spring telephone coil   around mobile phone to couple energy to phone patch antenna.