As I see it, the problem of balance is that after breaking the gate, you will be able to leave the system on the jump drive, but it will be impossible to enter your cluster.
So if you move the capital to the l-cluster and start building an Aetherophasic Engine, then it will be impossible to stop you...

maybe have it as an option somehow

proposal: Do not let the L-gate get removed from the cluster, but allow removal of all L-gates except the last one still existing elsewhere. This way a player has a good flexible option to decide which of the galaxy's gates stays connected to the cluster, while a full gamey cut-off isolation isn't possible.