Here is what I think with respect to Lisa Irwin's abductor:
He may have been the one sitting in the pulled up, light colored older model sedan (like a Taurus or Camry) a week prior to the abduction and who both Shane Beagley and his grandmother thought strange. This person may have been monitoring the home to see when the best time was to strike. Homes targeted for home invasions and burglaries are often staked out one to two weeks ahead of time.
(Note: As far as I know, no physical description was ever printed here of this man. I have wondered if his description would be similar to that of the man Mike Thompson saw).
This man had asked Shane B. if he had noticed anyone walking around the neighborhood. It is possible that he may have been asking to see if he - or an accomplice who had been casing the area as well - had been detected. People staking out a property to find out movements will often walk around the area, possibly chit chat with people, pose as meter readers, pose as a door to door salesman, sit in the woods near a property and observe it, and very importantly, collect information about dogs in the area and when they are outside and back inside at night as well as get to know the dogs.
He would have selected the area because I believe it is a low income area which tended to have a fair bit of crime. Residents in more upscale areas are far more on the look out for strangers, suspicious people, and possible home invaders. There is also more security and camera surveillance in more upscale areas which is a cause for concern.
Shane Beagley had stated to Jim Spellman that he thought he heard something from the woods behind his home on the night of the abduction. I believe the Bradley/Irwin children also heard something, including tapping, although the time of that is unknown. Home invaders will often tap or lightly knock a door first to see if anyone is awake, then enter. He was also likely monitoring the home from the woods right behind the property and could hear them That is how he would know when to make his move.
If that was him on the BP Gas station video around 2:15 - 2:30 AM, then it very very well may have been him heading eastbound on NE Parvin Road, walking in the same direction of traffic in order to keep his back to traffic and naturally concealing the child. Then northbound on Randolph Road to wherever he was heading. On foot it could take roughly an hour to get there. He may have taken a rest or two on this way there to give his arms a break.
And if that was him, then he probably had the baby with him and had just abducted her. I'd go as far as to say the abduction probably happened at around 1:45 AM or 2 AM. I'm not sure if that first sighting was as strong as initially presented...the one at around 12:15 AM. It is possible they didn't actually see a child but something else the person was carrying.
Why walk? If you are going to go all the way and take all the steps of watching someone and monitor a property, and make sure there are no loose ends, the last thing you will want is a baby's DNA all over the inside of your car. You also guarantee no reports of suspicious vehicles will be reported the next day, and definitely no amber alerts. This is someone who knows the score.
He could have taken North Bennington..a shorter route, but there would have been too many residential properties along the way. North Randoplh had more industrial properties than residential.
If the phone call were in fact no more than 1/3 of a mile or so from the house at all times, including the ones around 3:30 AM, then the person making the calls and the person adducing the child are different. Someone probably swiped the phones that night while they were in the house. It would be hard to come forward because then you could linked with a child abduction.
My impression is that he is very logical and well organized, although highly, highly criminal. He may have a military or law enforcement background. He has likely robbed before and is very well experienced. He was probably hired by someone linked to black market or shady adoption practices, such as brokering children from poor parents, running Christian programs for young mothers to give up their children, and so on.
If S.Beagley by chance ever reads this...what was the physical description of the man in that car?