I'm going with one of three general theories:
#1 It's a neighbor who saw the way the girls went into the park and followed them in that day. Came up with some ploy to get them to go quickly to the neighbor's house. The girls had probably spoken to the neighbor on their rides before (at least Elizabeth). It's easy enough to think of reasons the girls would drop their bikes. In that scenario, the girls had gotten inside the gate and left the purse where it was themselves.
Which neighbor has the house for it (nobody else home), the car for it; did anyone wash their car trunk or any of the other sorts of clues that were used in other cases? Those are questions for folks who would know, so basically rhetorical here
#2 It's a pedophile who went to the park for this purpose and didn't care which little girls he lured (maybe she, but much less likely). In that case, where would he park? He'd have to be familiar with the park and close neighbors, so he's local to at least a certain degree. How did he know that the neighbors were most all at work? He's been seen in that neighborhood before. He's also smart and not as impulsive as these perps can be. He had the girls throw the purse because he had the presence of mind to think of the cell phone. Did he even know about pings? This is a fairly smart perp, imho. He's probably a cool cucumber in real life and knows he doesn't look out of place. Does he look like a dad of the girls? There's an age range there. Maybe he looks like the grandad, even? What would he say if someone asked why he parked where he did? He'd have a reason ready.
#3 The opportunity perp. This one may have parked in a different spot (or may have originally and moved his car upon watching the girls). He didn't know he'd see the girls where he did that day. He wouldn't have been there as long, possibly. Or there's a very good chance that folks saw him doing whatever it is he does at the park. Does he fish? Why was he there that day, that time? He may be more impulsive because he could have just gotten 'lucky'
So those are my thoughts in case it helps locals think of who to look at or what they might remember that could be helpful. This case may be one that is solved by a parking ticket, imho. It's happened before!
The girls really could be alive. Where would someone like this take them in that town? Summer homes or fishing cottages are some thoughts I had. Prayers for the girls.