Do Not replace coax with more RG-59 if you can even find any , only use new RG-6. The really old coax has a foil shield that was not bonded to the foam or if you have the really old stuff , the plastic that is between the loose foil shield and the center wire. . Or even the old coax that has no foil shied , just braid.
I wonder if one can even buy those old split connectors with the separate crimp ring. . Years ago the phone and coax wiring was all done loop/daisy chain , what a nightmare !