The minimal recommendable amount of side bearing at the nut is something
people seem to not entirely agree about, if I understand correctly. I don't
really see the problem. There's always the chance to get a sufficient
_downward_ angle.
Also on these pictures one _can_ see at least _some_ side bearing onto the
pins, even though it is a little difficult to really get an idea how much.
In this setup, it seems to me that a bridge or nut with the right shape
[see one of David's messages]sufficiently divides the strings.

The side-bearing at the bridge seems here pretty okay, if not excessive. No
need to change something there, I'd say. [oh, and: I don't find this 4' and
8' string distribution strange].

Whatever can be said about the above observations, I would in any case make
some, no: many, tests before starting to drill random holes.
The string bearing against single nut pins can for example be increased
manually for a test, and the resulting sound will perhaps already tell the
story.
Or, strings might simply need de-rusting. The ones on my French Double
started to sound dull of late, and I removed the rust with good results.

Actually, considering the various techniques and advices of bridge-or-
nutpin mounting I've heard in the times of the first Historical-Zucker-rush
in Germany, I suspect that some of the pins simply are not tight enough
[euphemism for: "loose"]. This may come from holes that were too wide right
away or not exactly cylindrical as a consequence of a poor drilling
technique, or from wood shrinkage or whatever else, you name it. This is
not uncommon, really. If this now happens in combination with relatively
little side-bearing, as we see it here [more side bearing would perhaps
bend the pins against one side of their hole and thus reduce the problems
associated with looseness], the resulting sound can be pretty dull.

So more tests can be made: A heavy suitable piece of metal can be put onto
the nut pin of one of the dull strings. If the pin is loose, the tone
should be less dull with the extra mass stabilizing the pin. [However, the
same test is problematic on the bridge, as it also impedes the soundboard
from doing whatever soundboards should do. But one could at least try if
one can hear a change when stabilizing the pin in some creative manner].

Nut pins can be easily replaced using slightly thicker nut pins, so let's
hope it's not the bridge pins that are loose. I wouldn't know what to
recommend for the latter's replacement. You can't hammer on the bridge of
an unsupported soundboard in a completed harpsichord, and _pressing_ the
pins into holes of exACTly the right width is one of various possible
causes for loose pins...
Tilman