I can see how you arrived at your conclusion. I am not convinced but you explain your line thinking well.
I think Lily popping in to the adults' bedroom several times was because she and Jack were being left to their own devices. Probably hungry, possibly even unaware they were not being sent to school that day, because neither adult reports interacting with them in any meaningful way that morning. What bother me I guess is that I don't buy the kids are sick story. I think mommy was tired after a long day and didn't want to get up and get them ready for the bus. If one of the children was genuinely sick I guess the argument can be made that the reported "cough" could be heard throughout the night and therefore MBM knew without getting up to check on her two eldest that she was keeping at least one home so why not both. But nobody got up to address the needs of either child, sick or not? That troubles me, especially if one or both were sick or still getting over a bug.
As does the children not being changed into PJs although not as much because it does sound like a busy long day was had and I myself have on occasion allowed my littles to simply fall out wearing their day clothes. Although MBM reported putting both to bed and her version of that doesn't suggest they were sleeping already when she did so.
As to the children maybe knowing they were going on a secret adventure, at their ages, with their rambunctious natures, could they really be trusted with such a secret? I don't know that I think that any adults who knew these children and were part of some planned "extrication" from the property would be able to trust them with that information. Not to mention why on earth would they still be hidden? To what end? With all this publicity and a huge investigation going on?
I cannot recall where but I have read that it wasn't uncommon for Lily to have her backpack close at hand. No time to find a link so take it as a rumor if you want, but it tracks for me. Children like to have pockets and purses and backpacks IME to collect and keep close their "treasures"
I don't think they were abducted (stranger danger/random)
I don't think they were spirited away by some adult known to them (extended family member)
I don't think they wandered (although this and the next are to me the most likely answers at this point)
I think they are in those woods still, not alive, and I feel they didn't get there by themselves ( most likely IMO)
and I don't know that they will ever be found unless it is by happenstance a decade or more from now and that makes me very sad. I wish I believed your theory as it would mean the children are still alive somewhere, Jack collecting bugs, Lilly squealing with delight at something. But I don't