I think this a very thought provoking thread. Nicely done.

Now a few ideas I had..

Would it not be better to attemp to use distance as a measure for time? If you can find an equation that relates to the relative expasion rate of the universe without using the factor of time then you could substitute time with distance. I realise that to calculate the rate of anything you would need time, so i propose instead of trying to work out the expansion over the entire life of the universe only calculate the rate over a known time period.

This may sound a bit pointless, but if you then use that to calculate distance of expansion, you should in essence be able to work out the total expansion and then the time from that??

I am most likely very wrong as I FAIL epicaly at maths. I dont know, you should try it and see if it works.