Summer Solstice Calculation Questions

I was playing around with Starry Night Pro 5, and I thought I'd see if
I could determine the exact time of the summer solstice by watching
the solar coordinates. With SNP, you can select the sun, bring up an
info panel, and then watch the RA and Dec change as you run through
the clock time at the speed of your choice. I saw some things that I
can't explain, and I hope somebody here can help me.

First, in case my problem is with fundamental knowledge, tell me if
I'm wrong about any of these assumptions:

1) The solstice occurs when the sun reaches its maximum declination of
the year, which should be around 23.5 degrees N. The declination
never decreases between the vernal equinox and the summer solstice,
and never increases between the summer solstice and the autumnal
equinox.

2) The sun's RA at the solstice should be very close to 6 hours, but
since the RA is defined by the vernal equinox rather than the
solstice, the solstice may not occur at exactly 6 hours.

3) The sun's RA and Dec do not depend on my location, so if I read in
an almanac that the solstice occurred on June 21 at 8:26 AM EDT, I
need only correct for my time zone, rather than fractions of a time
zone (as I would if I were trying to calculate my local sunrise, for
example).

4) SNP has two sets of RA/Dec coordinates in its info panel, one
labeled J2000, and one labeled JNow. I assume that JNow will be more
accurate for current observations.

OK, assuming all that is correct, here is what I found. All times are
EDT.

1) On June 21, the maximum RA reached was 23 degrees and 26.386
minutes. This was maintained from 2:00 PM to 3:16 PM EDT. The
almanac says the solstice should have been at 8:26 AM EDT.

2) When I ran the time backward from there, the declination slowly
decreased, but it hit a minimum (when it was 23deg 26.314') that
lasted from 2:03 AM to 3:39 AM of June 21, then it began to increase
as I went farther back. It peaked at 23deg 26.332' from about 7:37 PM
to 8:20 PM of June 20, and steadily decreased as I went earlier than
that..

So if SNP is correct, there were three solstices, i.e. a max on both
the 20th and 21st, and a local min between them. I could understand
if round-off errors produced fluctuations right around the true
solstice, but I can't understand
a) the absolute max being nearly six hours off the published time,
and
b) apparently smooth progressions between two maximums nearly a day
apart.

Any explanations, or pointers to URLs, appreciated.