I think there are two main aspects to be considered.
1. Upadana plays a big role. Again, there are two instances where upadana comes to play.
– The first is when one gets a human bhava upon exhausting kammic energy in the previous bhava. For example, if a Deva dies and grasps a human bhava, that is according to “upadana paccaya bhava” at the cuti-patisandhi moment.
– The second instance is when a human gandhabba enters a womb. This is the case that Dawson is addressing. Here again, upadana plays a big role.
2. As we have discussed in the section, “Concepts of Upādāna and Upādānakkhandha” upadana plays a major role even during life with a human body.
– In particular, see “Generating Kammic Energy in the ‘Upādāna Paccayā Bhava’ Step.”
3. A gandhabba is drawn to a womb based on many factors. As you pointed out, parents’ “gati” need to match. The other major factor is the upadana of the gandhabba. A gandhabba is mostly drawn to an environment that he/she has a liking for. There are several accounts in the Tipitaka that make this clear. I don’t have the sutta references (maybe those who know can post), but a few are the following.
– The “Tirokuṭṭa Sutta (Kp 7)” describes how a gandhabba of a recently died person is drwan to that same home in many cases. A reasonable English translation: “The Beyond the Walls Discourse”
– Another account that comes to my mind: There was a bhikkhu who was very fond of a certain robe. His attachment (upadana) for the robe made him be reborn a tick on that same robe. In that case, his kammic energy for the human bhava was exhausted. His upadana for the robe (combined with other kammic factors) led to that extraordinary rebirth.
– Another factor is the following: When we talk about “gati” it is not just lobha gati, dosa gati, and moha gati. Other habits/tendencies come into play. This could be the reason for most rebirths accounts by children indicate that previous births were in the same region with similar customs, tendencies, etc. (as I mentioned in my previous post, per Professor Steveson’s studies.)
– It is a very complex subject. This is why only a Buddha is capable of analyzing kammic effects for a particular situation.
The other factor that comes into play is a technical one.
4. The universe in infinite and there are uncountable “10,000 world systems” or lokadhatu in the universe. I have given a brief description in the post, “Buddhism and Evolution – Aggañña Sutta (DN 27).”
– Even a Buddha can travel (or can communicate) only among those 10,000 systems, and not beyond that. Others have access to much smaller parts based on their abhinna powers. See, “Cūḷanikā Sutta (AN 3.80)” The English translation there is not that good: “80. Lesser”
– There is an account in the Tipitaka that describes how Ven. Moggalana “got lost” while traveling through the lokadhatu. See #18 of the post on Agganna Sutta.
– The point here is that it would be impossible that a gandhabba to cross over to other “world systems.” Even birth in a different planetary system within the 10,000 systems is highly unlikely. As we saw above, the rebirths of a gandhabba are highly localized.