I'm uncertain how to differentiate this properly from the transitive
“swallow” (tulcti).

For the intransitive use of “swallow”, AHD says:
To perform the act of swallowing.

For the intransitive use of “gulp”, AHD says:
1. To choke or gasp, as in swallowing large amounts of liquid.
2. To swallow air audibly, as in nervousness.

Using swallow (gulp) could be misleading in that it seems to have to do
with gasping. On the other hand, swallow (perform the act of swallowing)
is sub-optimal in that it's too long, and uses the “swallow” morpheme
itself, rather than a synonym.