Sharing the same language and social background would make military occupation more difficult, as it reduces the ability to other the occupied population. It also makes it easier for insurgent elements to infiltrate your own units. For an example of this, consider the infiltration of Iraqi units by insurgents and the ensuing problems they caused.

As for training and "better guns", the service weapon of the Army and Marines is the same weapon system family as is the most popular rifle in the United States: the AR15 (with military variants, the M16 and M4 carbine). Additionally, private owners are likely to have optics on par or better than are available to servicemen. And better-maintained weapons--you don't have to look far to get stories of infantry complaining about their gear. During the day, they'd be about equally matched individually. At night, NVGs and thermal sights would give the occupation forces an edge.

The infantry "better guns" that are out of reach of civilians in your scenario would be things like anti-material rocket launchers (AT4, SMAW) , grenades, and LMGs (M240s, M249s, etc.). With the exception of the rocket launchers, all of those are things that can be improvised or worked-around with the correct doctrine.

Rocket launchers, and more generally the air support and artillery that forms the true bulk of American land warfighting capability, are things that are vertboten when used against civilians. There's no credible armored targets requiring their use (except for perhaps captured law-enforcement surplus MRAPs) and so their deployment against a native insurgency would likely fall outside of the rules of engagement. Additionally, calling in airstrikes on insurgent positions in American cities has severely negative long-term implications for peacekeeping.

In short, fighting an urban or even exurban native insurgency the US military would possess only a slight material and technological advantage and even that would likely be severely undercut by having to follow very conservative ROE unless they wanted to rile up resistance further.

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As for your remark on historical references, if you want something a little more contemporary and probably more reflective of what we'd expect to see in your hypothetical scenario, please consult the history of Ireland in the 20th century.

Your remark on "overweight American gun-nuts" is misinformed. I know that's a popular stereotype, but it is neither accurate nor even useful. Again, the sort of engagements we'd expect wouldn't be "Let's hump our gear ten miles to the AO", it's "So, after work tonight, let's do this mission on the local garrison". To be blunt, for that style of warfare, you can use women, children, fatties--anybody that can hold a gun.

Also, on your last point--they have developed countermeasures to things like mortars and counterbattery fire and whatnot.

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Underscoring all of this thought experiment is something you're missing: in a supposed US insurgency, the huge non-combat advantage of the armed forces goes away. Our adventures abroad are backed by a logistics system and lift capability that boggles the mind, only made possible because we can keep all the ruckus of battle away from our airbases and factories and transportation hubs. In an insurgency, that massive advantage--one that's nearly taken for granted in the last two decades of warfare by our populous--disappears.