DB> the TWOK.  More specifically, does anyone have an estimate on the
 DB> amount of time that's supposed to have passed between these two movies
 DB> in "Star Trek" time?
The best indication is that years passed -- as many as 14 or 15.
Establishing dates in Star Trek is difficult because of contradicting
statements.
Here is one broadly accepted scenario:
In The Neutral Zone, Data said the year was 2364.
From various episodes, it is clear that Star Trek employs a "one season
equals one year" formula.
In Sarek, Sarek's age was given as 202, while in Journey to Babel it was
given as 101.  This places the second year of TOS in 2266.  At the
beginning of TOS is was clear that Kirk was fairly new to the command of
the Enterprise, so the five-year mission probably ended around 2269.
A reasonable time for a refit might be a year or two, so TMP would be in
the 2270-71 timeframe.
In Encounter at Farpoint, the announcer said "78 years have passed"
since the days of Captain Kirk.  The Movie Series at the time was in the
STII-V sequence, which are all set within a few weeks or months of each
other.  You get 2285-86 for this range.
A few other details in various episodes support this 2271-2285 gap.  But
again, there are discrepancies.  For example, the stardates for TMP and
TWOK are very close together.  
YMMV.  :-)
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