Indexical Paradoxes

I just fell across a fascinating digression over at Maverick Philosopher:

'It is now tomorrow' is incoherent given that 'tomorrow' is a temporal indexical the referent of which is the day after the day on which the indexical in question is tokened (uttered, written, etc.) Or can a word like 'tomorrow' function both as an indexical and as a rigid designator?

Strange as it may sound, I think this might be possible. (At least, it might take as its 'base index' some time other than the time of utterance.) Consider the following piece of (bad) fiction, which I will entitle Blackout:

It is late at night, and you fear that you are being followed. You turn around, but too late -- there is a dull thud as you are hit on the head, and everything goes dark.

It is now tomorrow. You feel groggy and disoriented as rays of sunlight slip through your squinting eyelids. The End.

Now, it seems to me that, within the context of Blackout, the sentence "It is now tomorrow" makes perfect sense and even sounds fairly unremarkable. (Quick survey: do you agree, or does it intuitively sound 'wrong' or 'unnatural' to you?)

I presume that, in this context, the word 'now' is indexed to the time of utterance as usual, whereas the base index for 'tomorrow' is instead taken to be the previous moment of narration. Or something along those lines.

A similar phenomenon occurs when one stays up past midnight and wryly observes, "Hey, it is now tomorrow!" (BV's original remarks were inspired by such an offhand remark from Jim Ryan.) Again, the base index (for 'tomorrow') is not taken to be the time of utterance, but rather, the day that has just passed. One might dismiss this as merely idiomatic, and not a proper - semantically coherent - sentence. But I don't see why one couldn't just as reasonably conclude that indexicals really can take as their 'base index' a time other than the time of utterance.

I'm put in mind of the complex tenses, e.g. "By the time I'm a grandparent, I will have had children." The "had" indicates a past tense, but relative to the future "will have", rather than relative to the present as is normally the case. I don't see why we couldn't treat indexicals similarly. The base time used to index 'tomorrow' is usually the present, but perhaps it can also take other bases, in the appropriate contexts (e.g. the examples above)?

One last thought: it seems to me that the sentence "I am not here" has a similar appearance of paradoxicality to "it is now tomorrow". Do you agree? Are there any contexts in which the sentence might be true when uttered? Can you think of any other sentences like this?