I found an answer, I don't think it's optimum, but it might be.
Using
ModuleContext.ModuleId/PortalId/TabId
and
ModuleContext.PortalSettings.UserId/UserInfo

These look like they will work, but it seems a lot of typing to get the UserId, which I accessed by 'UserId' before.

...
Why yes, yes it can.

Though, I'd have to do that for each control [View, edit, settings, ect] and I hate to have duplicated code like that. So I was hoping for an alternative way to 'wrap' it for simpler code.

I've worked on it a little more, and I got a solution I can accept. I think there is a slicker way, just not sure what it is yet. :)

I have a common code file, which I created a Module class, where I pass in the ModuleContext to the constructor and assign the values. I then declare it as a variable in my control class, and initialize it in page load. That way I should have it initialized and available 'everywhere'. I just access them by
module.UserId
which is about as best as I'm expecting, unless it's exposed in the (I)ModuleView class.

It'll work, but feels a little hackish, but reduces the duplicated code.