a modal question

So here's a question about modes not often asked as far as I can tell. As a bit of prologue let's assume that we all know a bit about modes: their structures and the sorts of chords (triads/sevenths) that they produce. Armed with such knowledge we could easily address the following question: what is the mode of the following progression?

G7 | Fmaj7/G | G7 | Fmaj7/G | (repeated)

This is fairly unambiguous: it's G mixolydian. An analytic play-by-play might go like this (here the paths are many, but this one). The notes of the chords in question are:

G7: g, b, d, f
Fmaj7/G: f, a, c, e (with a g in the bass)

Now we put these notes in order to see if they form a scale. We could start anywhere, but since we notice that G is prominent (it's the bass note in both chords) let's put it first. We then get:

g, a, b, c, d, e, f

We now have a 7-note scale. Since there are no sharps or flats we can easily conclude that it must be some kind of mode of C major. G is the 5th tone of C major, and the mode on that tone is the mixolydian. (We could also have deduced mixolydian from the tones themselves simply by analyzing their relationship: 1 2 3 4 5 6 b7).

OK, so far so good. But here's the question part: What if the chord progression is changed just slightly to this:

G7 | Fmaj7 | G7 | Fmaj7 | (repeated)

That is we no longer have a grounding G bass note -- instead we have 2 different chords. If they're both of equal length (and consequently equally prominent) what is the mode now? Can we really safely say that it's G mixolydian? It seems that it might just as likely be F lydian. And really the first or last chords may not give any aid in determining: the first chord might likely lead to the real tonal area later, and the last chord might produce some kind of unresolved, "hanging" effect.

Again, we could have a chord progression as above that does emphasize one modal area, by rhythm or perhaps even the melody. But my main point is that in no way would we be on sure footing in certain circumstances when attempting to answer the question of mode.

And, by the way, why would we ask such a question? Because if we're improvising we have to have some way of dealing with the music at hand. And this goes to my over-arching view of practicality. If someone were to say, well, given the 2nd chord progression above I'd just play a C major scale, I don't see how that's a real problem. Also if one were to say that there's no single mode and that s/he would switch between mixolydian and lydian, also not a problem (though if the tune were up-tempo it might be difficult to manage 'switching').

The question is also interesting from an historical point of view: in music around Mozart's time an ambiguous key center would have to be deliberate (like in a developmental section) or it would just be bad music because projecting a key center was the name of the game. In our time that's just not the case: ambiguity abounds and we can bask in it, but also have to deal with its implications...