A few of those suggestions seem a lot more "barbaric" than the government enforcing anti-monopoly laws. Imagine administrators, researchers, or whomever else works for the government having to change up their entire work routines and use a search engine they may ethically oppose because the government is trying to force fairmindedness. And the government should pick and choose patents to invalidate because the inventions described are too popular?

Imagine a 60 year old lady with stock in a company that has had its value destroy by anti-monopoly laws...

Imagine how much money flows out of investors' pockets and into the pockets of government insiders and lawyers during a big antitrust lawsuit..

Well, poor them. Regulatory risk is just one of the risks of investing. Yes, it sucks that some of them are going to be the retirees of the world, but again, that applies generally to all investing. When you're making public policy, you have to put the individual aside and focus on the macro impact.

Now imagine all the value and money-making opportunity created for those investors by having a healthy and active competitive marketplace.

You could make the same argument about any company breaking laws and regulations or at least operating in grey (eg. AirBnb, Uber,...)

Funding research into search is good but the other options are impractical.

If 4 is doable, it would take many years and involve many lawyers and potentially wind up achieving nothing.

1 and 2 involve directly interfering in the operations of other organisations in order to erode 0.000001% of Google's business. How would you enforce this anyway?

This isn't about the lack of competition on the search engine market as it is about a single entity holding as much financial and political power to undermine every single one of your suggestions with ease.

It isn't barbaric to break up a company - at all.

Companies operate in our society, and they impact the citizens of our society. It is reasonable to directly stop a company when it is working against the shared values of our society.

Really, I would argue that it is barbaric to force a society to live with a company which ignores the wider interests of society.

Silly use of persuasive words on the part of the OP. Barbarians don't have corporations nor anti-trust regulation. All of the "market forces" remedies that the OP suggest are just the sort of thing that monopoly power makes ineffective. If Google is a utility like the phone system circa 1970, then the solutions suggested are analogous to addressing AT&T's monopoly by forcing government employees to use ham radios one week and carrier pigeons the next. Monopoly power means that consumer choice has been reduced to the choice to take it or leave it and all the suggestions are simply that; take it or leave it.

Maybe if you owned one you'd feel differently.

Can I reach into your backpack and crush your bag of potato chips?

What's the matter; all the baked potato material is still there!

If my bag of potato chips is demonstrably and deliberately harming the lives of many real live people, you are welcome to crush it.

(Not that all corporations harm people. But some combination of "the way we tend to structure them" and "human behavior in large groups" seems to make them a lot more cavalier about collateral harm and negative externalities, particularly as they get big.)

I'm pretty sure you can understand how much of a false equivalency it is to compare a bag of chips with a powerful entity like Google.