Grammar

No. That's an awkward construction.

A native-speaker of the language would say, "For the last year we have been here."

Or.
We have been here for a year. "The last" is unnecessary.

I humbly disagree. It is necessary for the sake of clarity.

Why is "last" needed in this sentence? "....have been here" implies it's the current period.

Because it was this last interval of 12 months not some otherprevious 12-month period that we were here.

How can it be other than the current 12 month period?



Sounds like a present participle to me.

Very easily. Here implies no timeframe.
For example:
"Custer's last stand was here."

There is no specific timeframe that implies it was now or even a recent event.

Furthermore, if the following statement were possible, "For the year 2012, we have been here", then stating last year would clarify the matter.

It's the 'best' assumption, because it doesn't say otherwise.

Your example, is time and place specific.

Date and place: June 25, 1876, and place was Little Bighorn. That's the 'here.'

Furthermore, if the following statement were possible, "For the year 2012, we have been here", then stating last year would clarify the matter.

Shouldn't that read, "For the year 2012, we have been there......."

I'll let others comment. I don't seem to be getting across so I'll be silent for a bit.

It seems a simple matter of present and past tense.
Also, I'll admit I can be 'dense' some times.

Let's add the question.
'How long have you been here?'
'We have been here a year' - We have been here 'for' a year - We have been here for 'the last' year'

A simpler response would be 'A year, One year'
An extreme response would be 'Without wishing to be overly enthusiastic about having to clarify my positional location within the commonly used calendrical temperal-zone - I would, all things, considerable, taken into consideration, announce, verbally, via my vocal ability, unto your, curious, self that we have been at or about this location, on a regular basis, for no longer or no less than one year.'

Without knowing whether "we" have ever left "here" assumes a constant.
Otherwise, the reader assumes they left and came back. I don't see it that way.