In the Server Merging Thread in this forum there were already a few suggestions that thought about compensating the player for all the time/money they invested into a server that is now dead. For example with titles or skins/portraits.
I suggest to hand out free months of Patron as a reward for old accounts on dead servers.
When a server merge happens (whatever method ends up being used) all merging players get the choice of either following the merge or reseting/trading their account in order to receive several months of free Patron on a new server of their choice.
The amount of months you would get for free would be somewhat depending on how much time you invested in your old account.
It should however not take into account the money you invested directly but rather your current Power or the Building/Research Time you invested.
One example would be:
The combined building time you invested in one server in months rounded down.
Since you never have buildings queued at all time (and because of the rounding) you will never achieve an endless cycle where you will always have Patron.