A law firm that has decided to represent you has to handle your case using diligence, no matter what internal hirings and firings may be going on. In other words, they have to make sure their attorneys are handling your case diligently.
That being said, MSA's can take many months to complete, and this is outside the control of the attorney on your case. While there has been a delay in your case, the question remains whether you have any damages because of it. Have your attorneys breached their contract
with you? By not keeping you updated and not assigning an attorney to work diligently on your case, you have an argument that yes they have. However, a lawsuit against a law firm for return of a fee is much less likely to be successful where the attorneys have in fact performed services and obtained the settlement agreement
(but have failed to get the settlement funded and you paid). Rather, you may be more successful in suing the attorneys for malpractice.
That being said, if you fire them now, what would happen to the settlement agreement? Can you finalize yourself? Possibly, but this depends in great amount on whether or not you have all the required paperwork needed. The settlement agreement which was awaiting the MSA is a document which is often very lengthy and complicated. So, proceeding without an attorney is probably not a good idea.
A person in your situation might try filing a grievance with the California State Bar complaining about these lawyers and see if this would put some fire under your lawyers to get the job done. Firing them now and either attempting to do it yourself (which will be very difficult) or getting a new attorney (which will cost you more in the end) will likely delay the funding of the settlement even further.