I don't see what time has to do with it, unless you are thinking of what you wrote below.
My thinking was that after a coin had ping-ponged back and forth without merging for 4 or 5 transactions you can safely merge it.
What is this off-chain signing?
Yeah merging can be solved that way, yet it is the forking due to giving change that can't be delinked. Nearly every transaction involves giving change.
Off-chain is where I create a transaction with 3 inputs from me and 3 from you. I sign it, send it to you, you sign it and broadcast it to the network. These types of transactions will be cheaper than using the built-in block chain for bids and orders.
How about if miners are tumblers wouldn't that solve the problem to great extent?
https://bitcointalksearch.org/topic/coinjoin-bitcoin-privacy-for-the-real-world-279249
E.g. Using chaum blind signatures: The users connect and provide inputs (and change addresses) and a cryptographically-blinded version of the address they want their private coins to go to; the server signs the tokens and returns them. The users anonymously reconnect, unblind their output addresses, and return them to the server. The server can see that all the outputs were signed by it and so all the outputs had to come from valid participants. Later people reconnect and sign.