Nishmat's Women’s Health and Halacha deals with some of these issues.
The page on “Egg Donation & Surrogacy” contains this information:
There is no clear halachic consensus as to whether the status of the
child as a Jew is based on the genetic mother, the birth mother, or
both. Using a Jewish surrogate and/or a known Jewish egg donor is
preferred when possible, so that there is no doubt about the baby’s
In practice, babies born from procedures involving non-Jewish
surrogates or egg donors often undergo conversion in early infancy to
ensure that they are considered Jewish according to all opinions.
Since they are contractually obligated to carry the baby, surrogates
cannot be anonymous. In order to rule out an unwitting future marriage
between halachic siblings, Jewish egg donors should be known or listed
in a registry. (At this point in time, the medical establishment is
less concerned than the halachic establishment about the chances of
sibling marriage, because the statistical odds are very low.)
Marital relations are not involved in in vitro fertilization.
Nevertheless, the surrogate or donor should ideally be a woman for
whom relations with the genetic father would not violate a serious
sexual prohibition (giluy arayot), since some halachic authorities
argue that that would have negative halachic implications for the
child. Therefore, a Jewish surrogate or donor should not be closely
related to either parent (e.g. not a first-degree relative), and
should ideally be unmarried.
Some authorities may permit using a married surrogate on a
case-by-case basis, following individual consultation, because no act
of prohibited relations is involved in these procedures.
At this stage, Nishmat’s Rabbis do not make rulings on the question of
whether it is permissible for a married woman to be a surrogate,
though they recognize rulings from other halachic authorities.
You ask, “whether the label of incest ("forbidden relation") is one of the act of the physical bodies (intimacy), status of the involved individuals (regardless of the method of involvement), or the underlying event (conception regardless of location).”
From the text above, I deduce that a case can be made that intimacy is not essentially the determinant in giluy arayot but that nevertheless the possibility of an association with giluy arayot should normally be avoided.