While a signing ban is a decent idea, you're still left with the possibility that other teams would object that, hey, they too would be willing to ride out a short-term transfer ban in order to field four DPs for as long as they felt it was advantageous, but they have no opportunity to do that this close to the end of the rostering period.
Anything which allows LAG to proceed with four DPs on the books has this same inherent problem: a short-term competitive advantage to LAG (your opinion of GDS notwithstanding) not offered to the other teams in the league.
I think the way this could end is MLS buying out GDS's contract and releasing him and then (possibly) fining or otherwise punishing LAG financially (or appearing to).