I wonder how you decide to measure things in years on this scale. I mean, in about 10^10 years, the whole concept of a 'year' will stop to exist. What will you do then?
I would expect something like 'tera-seconds', or something related to a cosmological constant but at cosmological scale, like the time to decay hydrogen or number of caesium vibrations for example, but then scaled at AU scale. A value not related to time or space.
A year is defined in multiples of caesium vibrations. Not originally, obviously, but in this context it is. You cannot nearly measure any of these time periods precisely enough that any of this matters anyway.
I would expect something like 'tera-seconds', or something related to a cosmological constant but at cosmological scale, like the time to decay hydrogen or number of caesium vibrations for example, but then scaled at AU scale. A value not related to time or space.