Dear Madhavji,
Have you checked the supersite of IIT-K which has the text for all the important commentaries including Śankara and Madhva.
https://www.gitasupersite.iitk.ac.inAlso the following paper appears to discuss the topic in detail, which I have only a snippet view access on google books:
Bhavani, Sudhindra: Is Arjuna amadhyamadhikarin? [Engl.]. In: Studies in Indian history and culture: volume presented to Dr. P. B. Desai ... 1971. - pp. 412-415
The following snippet appears to confirm Sankara proposed Arjuna as a Madhyamadhikarin.
Madhva has therefore, hastened to correct this impression left by Śankara and dispel the myth of Arjuna's being a Madhyamadhikarin. At the very beginning of his Gīta-Tatparya he hails Arjuna as a front rank Adhikari (Uttamadhikari) and as the best beloved of the Lord (Atmanah priyatamah).
https://books.google.com/books?id=H821AAAAIAAJ&dq=madhyamadhikarin+arjunaRegards,
Suresh.