How “kosher” Nāgārjuna is from an EBT standpoint depends on how one interprets what he’s doing in the MMK.
If you take the Kalupahana route and just see him as a return to the middle way of the Buddha, he’s pretty kosher. I think his anti-foundationalist views and critiques of svabhava are pretty compatible.
But I’m not sure if all his ideas are sourced in EBTs or can be supported by them, I’m especially thinking about his idea that nirvana and samsara are not different (at least “ultimately”):
na saṁsārasya nirvāṇāt kiṁ cid asti viśeṣaṇaṁ
There is nothing whatsoever of samsara distinguishing (it) from nirvana.
na nirvāṇasya saṁsārāt kiṁ cid asti viśeṣaṇaṁ | 19
There is nothing whatsoever of nirvana distinguishing it from samsara.
nirvāṇasya ca yā koṭiḥ koṭiḥ
(That?) is the limit which is the limit of nirvana and the limit of samsara;
na tayor antaraṁ kiñcit susūkśmam api vidyate | 20
Even a very subtle interval is not found of (between) them.
Needless to say, a lot of ink has been spilled and much yarn has been spun from this doctrine in Mahayana schools, but I am not sure if it’s “kosher” as per EBTs. From an EBT perspective, there is certainly a difference between the two and this is important, it is dukkha. If I recall, at least one explanation of this doctrine is that what Nagarjuna means here is that “ultimately” there is not difference between the two (since they are both empty).
Of course, this doctrine relies on the further theory of the two truths (which Nagarjuna and Abhidharmikas identified with samsara and nirvana, another innovation not in the EBTs). Nagarjuna was involved in working with this theory, which was invented by the Abhidharmikas (according to Karunadasa in his Theravada Version of the Two Truths). But IMO I think that the “two truths” model is not one which the Buddha taught, it was a later Abhidharma elaboration based on the idea of statements which are nītattha (explicit, definitive) and neyyattha (requiring further explanation). But for me, this teaching of the EBTs is not an epistemic or metaphysical theory, its one of hermeneutics. According to Karunadasa, sammuti (linguistic conventions) are not analyzed down into existents called paramattha (ultimate) in the EBTs. It seems like Abhidharma made up an epistemic and metaphysical theory which tied certain EBT ideas of hermeneutics and knowledge with a person’s understanding (arhats see the ultimate truth, paramattha).
This theory got all weird and essentialist in Sarvastivada, and Nagarjuna came along and critiqued it. But he failed to see that the entire theory is unnecessary and retained the “two truths” model, only modifying it. IMO from an EBT perspective, the best thing to do probably is to chuck this model, which is based on a misunderstanding of the Abhidharma. I know this is heresy to some Abhidharma people and to Mahayanists who worship Nagarjuna as a second Buddha, but this is just my own opinion. Another option is to just see this model as one possible interpretation of Buddhist epistemology, but not necessarily the only possible way of reading the texts.
So I would say the very idea of the “two truths” which is such an important and foundational doctrine in Madhyamaka, is somewhat problematic and definitely not the only way to read the EBTs. I don’t think we should be hamstrung by this doctrine to divide everything into “ultimate” vs “conventional” and so on when reading the EBTs. Especially since, the Sanskrit term samvrti means to conceal and hide, while it doesn’t seem like this term had the same connotation in the Buddha’s time. But at the same time I can see a lot of sophistication in the work of Nagarjuna, so I think he should still be read today (but not slavishly of course).