The wiring from the street is RG59, probably about 20'. All my wiring is
RG6, about 60'. One of the existing outlets has about 4' of RG59 from the
splitter, but the outlet that I tried the digital box on was all RJ6,
except the old RG59 from the street. I could change the outlet with the
RG59 to RG6 if necessary, and I suppose I could also change the wiring
from the street.

RG59 cable is not your problem. You will never tell the diffference between
RG59 and RG6 for short runs like you describe.

Don in Tracy, Calif.