The review in the Worcester Chronicle of 25 April 1896 clearly states that Elgar conducted the performance, and also conducted Guilmant's Symphony for organ and orchestra, with Hugh Blair at the organ. Blair and Elgar otherwise shared the conducting (the review is not clear on what, if anything, Elgar conducted apart from his own work and the Guilmant). The reviewer remarked that "Mr. Elgar can as gracefully handle the composer's pen as he does the bow of the violinist, and the conductor's baton". So in his home town in 1896, Elgar was known as a violinist and conductor who did a bit of composing on the side!
But, as you say, this does not resolve the mystery. Most sources, such as elgar.org., tell us that the choir and piano (2 hands) version came first, in 1895, and the orchestrated version a year later. There are recordings of the choir and piano (2 hands) version stating that it is the original version, so I think we can take it as a genuine alternative, not just a vocal score for rehearsal purposes. Certainly, the version with piano is viable and effective in a way that a performance of, say, Gerontius, with piano accompaniment clearly would not be. Though, in the absence of a named arranger, the default assumption is that Elgar himself did prepare the piano arrangement of Gerontius in the vocal score, so we can only hope that no misplaced authenticist will perform and record it in this form.
But, to get back to Bavarian Highlands, what I don't find is any reference to a version with piano duet accompaniment and, if the assertion by the conductor of the Roman performance that it is "often performed" were correct, I would expect to find traces of a few performances on the internet.