Richard Carrier is right when he says that, alone, ''brother of the Lord'' is not evidence of James being physical brother of Jesus because there is no way to overcome the ambiguity of the construct in the absence of more specific.
I think a case can be made that that ambiguity is deliberately sought by the interpolator.
Until now, the best case in favor of Gal 1:19 being a interpolation (together with its broader context Gal 1:18-24) is made by dr. Detering here.
(p. 24-25)Inventing this first trip the editor wants to prove, against the text, that Paul
did not delay entering into contact with the heads of the Jerusalem Church.
Against the above given explanation one might object: Why does the editor
heavily emphasize the fact that he hasn’t seen anyone but Peter and James,
since his interest is said to have been in connecting Paul as closely as possible
with those in Jerusalem? Moreover, why doesn’t his insertion follow even
more accurately the depiction of Acts?
Keeping in mind the editor’s task, these questions can adequately be
answered: We have to consider: in 1,17, Paul had explicitly denied to have
been in contact after his conversion with those, who were apostles before
himself. The editor now could erase this statement, – or reinterpret it. As a
skilled editor, who did not want to write a new text but to alter the extant one,
he chose the second way. So he reinterpreted 1,17 in the sense, that Paul had
seen Peter and James, yet not the other apostles. Because of the context, this
was a concession he could not dispense with. Though this splitting up results
in a rather artificial construction (as already B. BAUER noticed: did then the
other apostles happen to be on a journey? did Paul consciously avoid meeting
them?), Paul nevertheless was set into the Jerusalem tradition. Paul had seen
Peter and James and had been with Peter for two weeks! — that should be
enough to prove (to the Marcionites) that the Paul of Galatians had not any
more than the Paul of Acts received a special revelation and consequently was
not the subject of divine revelation in his own right. May then the report in
Galatians not fully be in agreement with Acts (9, 27), where Paul is conducted
to the apostles (the author surely meant ‚all of the apostles’) by Barnabas. It is
the logical result of the special task undertaken in this place by the editor: one
way or the other, he had to pervert the meaning of 1,17 to get Paul in contact
with the other apostles after all. And his depiction does not really contradict
Acts: by his construction he managed to explain why, in 1, 17, Paul
nevertheless could say he had not gone up to Jerusalem to those, who had
already been apostles before himself (in fact, he had not gone to all of the
apostles!) — and, the all important project, he had managed to confirm the
Catholic point of view.
But what Detering omits in his acute explanation is precisely what Richard Carrier disclosed in OHJ about Acts:
i.e. that the author of Acts presents certainly the idea that the early church would gather even fleshly brothers and sisters of Jesus, but is not able to better identify them by name (never saying that James is the brother of Jesus, for example).
If the interpolator knows Acts, then he should be ignorant about who precisely is brother of Jesus kata sarka because he would know only that some brothers of Jesus were Christian (but not their names).
This ignorance is reflected in Gal 1:19 (seen as an interpolation) but with an ambiguity that is basically anti-marcionite in nature and therefore deliberate.
Then after three years, I went up to Jerusalem to get acquainted with Peter and stayed with him fifteen days. I saw none of the other apostles but only James, the Lord's brother.
If the interpolator meant precisely James 'brother of Jesus' because he used the ambiguous expression ''brother of the Lord''?
It is a case similar to Gal 4:4 :
if the anti-marcionite interpolator meant precisely ''born of Mary'' because he wrote instead the more ambiguous ''born of woman'' ?
The question is answered if we see what happens in Luke 8:19-21.
As I say in this thread
assuming the Evangelion's priority, the proto-catholic 'Luke' inserted Luke 8:19 in order to read the next answer of Jesus ''who are my mother and my brothers?'' in a non-literal sense - as relative rejection of his blood relatives - contra marcionite interpretation that instead did read these words as an explicit absolute negation made by Jesus of his having a blood family.
According to marcionites, Jesus had absolutely only a unique family: the true Christians by faith.
(that means: no need, for them, to read ''brothers of the Lord'' in a epistle, but only ''brothers'').
According to proto-catholics, Jesus had a blood family but his true family is the Church.
A physical brother of Jesus can be also a Christian (therefore a 'brother of Lord' at the same time).
A physical mother of Jesus can be also a Christian (therefore a member of the future 'celestial Jerusalem', i.e. the allegorical Sarah of Gal 4 at the same time).
In this way it's explained Gal 1:19 as anti-marcionite interpolation: the interpolator did introduce deliberately the intrinsic ambiguity of the expression ''brother of Lord'' because he wanted to remember that James was mainly a Christian and yet could also be a blood brother of Jesus, so that now the riotous Paul not only submits himself to Peter, but bears eventually homage to a potential blood brother of Jesus, too.
In this way, Paul was so induced to recognize on the one hand the supremacy of Peter, on the other hand to recognize the possibility that behind a mere ''Lord's brother'' was hiding a blood brother of Jesus.
Note that the Catholic interpolator cannot insert 'brother of Jesus' explicitly because in that case he would risk of going against the 'Catholic hierarchy' who wanted a generic Christian still higher than any blood brother of Jesus (according to catholic interpretation of Luke 8:19-21).
For the catholic interpolator, to insert ''brother of Jesus'' means to go against the same words of Jesus in Luke 8:20 that rejected his blood family in favor of his true ''brothers'': the Christians. In doubt (because he didn't know, basing on Acts, if James was really the brother of Jesus), the interpolator wrote ''brother of the Lord'' in Gal 1:19, so to raise at least the possibility that James was a carnal brother of Jesus, in addition to being already a Christian.
The heretic readers of that interpolation would not understand at first sight if James was a simple Christian or the brother of Jesus (just like us, today!) so the most economic explanation that they would appeal was that James was both, but so recognizing the humanity of Jesus.
Their reaction, so as not to give victory to the Catholics, was to create Gnostic legends around James, then favoring ultimately the process of historicizing of Jesus.
If I am right, then Richard Carrier was able, in OHJ, to go back to the true meaning of Galatians 1:19 as the Catholic interpolator wanted to give to it : a deliberate ambiguity about the true identity of James.
If am right, then the original pauline epistles, if a historical Paul existed at all, didn't have Gal 1:19 and his broader context.