I don't think that genuine care for another, including one's own child, ever enters the mind of a psychopath. Becoming a father would have created an additional demand on his time, however, and might have reduced the frequency of his killing.
The two victims that he was convicted of murdering were found on November 2, 1993, and January 30, 1994, respectively. He is also the prime suspect in the murder of Sandra Costilla, who was found on November 30, 1993. We don't know the exact dates that those women were murdered, but any way you slice it, it doesn't sound like Johnny Boy had much of a cooling off period in between kills.
We've seen in other cases that getting into a relationship or getting married can reduce a serial killer's killing frequency, so I wouldn't necessarily expect Bittrolff to have kept that pace up for the roughly twenty years that he was active, but I would not be at all surprised if has killed more women that just the three mentioned above and the women attributed to the LISK.
I don't believe that Shannan Gilbert was a LISK victim, but the search for her shined a light on the LISK's stomping ground and might have caused him to go dormant, so there might not be any post-2011 victims. If there are any, the LISK might have disposed of them far from the old dump sites.
There is also a big gap in the LISK timeline. Jessica Taylor's remains were found on July 26, 2003, five days after she disappeared, and the Maureen Brainard Barnes disappeared on July 9, 2007. There was no known LISK activity during that four-year stretch. What was Bittrolff up to during that time period? Was he using an unknown dumping ground that has not yet been discovered?