No... they would last much longer than a week. I'm going to recommend some reading to you:
You don't go into neighborhoods, kicking in doors with guns blazing. They recently did that in Detroit to serve a warrant. Post Mortem: 1 dead 6 year old girl, 1 injured 72 year old grandmother, 0 arrests.
Think of it this way...
For every enemy, or (gang member), you kill, you create one. For every innocent you kill in pursuit of a gang member, you create 10 enemies. (Keep in mind, the people in the neighborhood KNOW who is innocent, even if you don't.)
These are hard problems. They defy simple solutions. In fact, the application of simple solutions to this PARTICULAR class of problems only creates more problems.
It describes the code (developed by Prussian jurist Francis Lieber) used by the victorious Union to suppress armed opposition ("insurgency") in the defeated Confederacy after the end of the American Civil War. If you compare its prescriptions to those in the "modern" counterinsurgency manual you linked to, you will see why the Union succeeded where present efforts fail.
You don't go into neighborhoods, kicking in doors with guns blazing. They recently did that in Detroit to serve a warrant.
No, you start by declaring martial law and enforcing a curfew. Santa Ana's gangs are a military problem, and they demand a military solution. If you're serving warrants, you've already lost the battle.
I understand that this is off the political map. That's the point. The kinds of policies needed to successfully defeat these gangs are anathema to prevailing civil libertarian views. But civilized 4th Amendment–style liberties only work when basic conditions of law & order hold; they don't work in a war. Indeed, when applied in a war, they only make things worse. This is why the present system, which serves warrants to soldiers in the opposing army, is complicit in their crimes.
It just won't work.
For instance... let's say you have a curfew... well gang members already ARE indoors by curfew! Minding their drug dens, which get maximum business during evening, (curfew), hours. In fact, drug gangs would LOVE martial law... because it would rid them of their chief competition... the low level, open air, street drug dealer. Currently, the only way they can get rid of those guys is through targeted violence. Which brings them trouble. Your recommendations would actually CEMENT the gang's hold on a given drug market.
You approach what you see as a war... but everyone else sees as a business. The police are having a lot of success right now disrupting business. The core of the strategy in NY was not "quality of life", as so many people parrot. Rather it was "disrupt business" wherever you see it. Even the "Squeegee-men" were targeted. And the results have been fantastic.
Now, are innocent people still getting hurt? Of course. But collateral damage is nowhere NEAR the level it was during the crack wars of the 80's and 90's. At the same time, violence is WAY down relative the crack wars. That's because we have gotten MUCH smarter. Well... most of us. Violence is down in places like NY, LA and even Chicago relative the crack wars. But places like Detroit persist with old tactics and have not made as much headway. Many of the "squeegee-men" equivalents still operate with impunity in Detroit. Which tells you that Detroit is not serious about cleaning up it's city. They only care to crack down on gangs with military zeal. Which is why they have the problems they do.