@DiamondMine
You need to stop taking them in. At all. Don't answer the door. Or if you do answer accidentally because you don't realise it's for your neighbour, then just say 'sorry I am going away for a few days in half an hour, and won't be able to give the stuff to them.'
I stopped taking in packages for neighbours maybe 5 or 6 years ago. Because of a few different reasons (including the ones you have highlighted,) but one main reason made me determined to never take anything else in for anyone else.
I signed for something once, (for a neighbour I didn't know who lived 4 doors away, and had moved in a couple of months earlier...) and they came to collect the item the following day.
Long story short, several weeks later, the company who had sent the item (which was valued in the mid 3 figures,) wrote to me claiming that this neighbour had said they never received their item, and that they had it on record that I had signed for it. I said 'yeah I did, but they came and got it the next day.'
The upshot is, it caused me a LOT of bother, that took several months to recover from, (people from the company who sent the item calling at my house, this neighbour and their extended family getting arsey with me, and denying they had had the item, being questioned by the police etc..., because I couldn't prove I had given this neighbour the item!)
It couldn't be proved that I HADN'T given it to them either, and there was a kind of stalemate situation.
I moved house several months after this incident (some 40 miles away,) and never heard about it again... But I will never ever take in parcels for people again. I also don't expect - or want - anyone to take mine in either.
I usually just don't answer the door if a delivery driver (for someone else) knocks, but if they do catch me (like I the garden for example,) I refuse, and/or make an excuse.