As I understand the examples, the question's own 3b ("The girls who John think he expects to be late") is preferable to 3a.
On pronouns and nonstandard agreement
First, I should note that there are two distinct steps to the analysis you outlined. Kimball and Aissen (1971) posit a dialect where the verb in a relative clause may agree with the wh- element when the main subject of the sentence is plural. Meanwhile, Henry (1995) cites Kayne (1989) as suggesting that the construction is impossible with a nominative pronoun, because (for Henry) nominative pronouns must agree with their verb. Henry provides these contrasting examples:
(4a) the people who Clark think are in the garden
[x] (4b) the people who she think are in the garden
In 4b, Henry expects "the people who she thinks are in the garden." So the verb has to agree with the pronominal subject, not who.
On multiple instances of who-agreement and consistency
Within lengthier constructions, Kimball and Aissen (1971) state that multiple verbs may behave in the same way, provided they are not interrupted by another who or that:
(5a) Where are the boys who Tom think Dick believe Harry expect to be late?
(5b) Lucine knows the people who John think it is surprising to that Bill makes ([x]make) money
One principle evident in examples is proximity versus interrupted usage. Kimball and Aissen and others I've consulted do not give examples where who is separated from the verb it agrees with by another verb. The example of multiple verbs in agreement with who may work because each usage follows in consistency from the previous one. Thus the following isn't likely because a speaker would not likely switch back and forth between "Tom think," "Dick believes," and "Harry expect":
[x] (5c) Where are the boys who Tom think Dick believes Harry expect to be late?
Using pronouns and following the expectations for consistency
Within multi-verb situations, it stands to reason that consistency with the previous verb usage would override the option to agree with who. So if the first verb following who agrees with its subject (as must happen with a pronominal subject), then I would expect the next verb to stay consistent with its subject as well, e.g.:
[x] (6a) The girls who he thinks John expect to be late
(6b) The girls who he thinks John expects to be late
In contrast, if the pronoun-verb combination came second, then it would be possible for the first verb (but not subsequent verbs) to agree with who. See the following, adapting 5a:
(7a) Where are the boys who Tom think she believes Harry expects to be late?
In theory, one could also move the pronominal example later.
(7b) Where are the boys who Tom think Dick believe she expects to be late?
In other words, the pronominal usage would make it so that consistency with the previous usage overrides the optional who-agreement behavior. In that paradigm, the original question's 3b is preferable to 3a.