Very cool graph!  But I'm not sure if it tells much of a tale.  There's no hint as to how many distinct Tx packets you are seeing.

I don't claim to be an expert on the Bitcoin protocol.  I only know what I've observed.

With respect to the long tail, I think that could happen if a node was offline when the packet originally traversed the network.  Later, when the node rejoins the network, it receives the Tx packet from one of its peers.  I think it retransmits that packet to each peer it subsequently connects with.

I think this may also occur as connections between peers flap up and down.  Doesn't each new "up" connection result in an exchange of some queued Tx data?

You said you had 1900 connections "at the end of the experiment".  I would expect a connection you made 20 minutes into the experiment to send you the transaction 20 minutes (or more) after the start of the experiment.  So, did you track the time between when you last connected to a peer and when the peer next sent you the Tx packet?

A useful overlay would be the time between when you first see a packet and the time when it enters the blockchain.  I think the slope of your long tail is partially dependent on how quickly packets enter the blockchain.