Dissatisfied but still intrigued, I fell back on a long-standing practice; think and list every word which rhymes well with "June", and every word/combination of words which could be pressed into service. It's evident that "round" and "gown" were acceptable (and, incidentally, work perfectly in some Scots dialects).
I stopped at "tomb". This seems so likely - in logical terms - that it seemed worthwhile to throw the idea out there and let others have a go at reconciling the sounds of the line into something cogent and not convoluted. Or maybe I should throw the idea out.
Lord Byron's work was widely read, though perhaps not by all orders of society. In his "Childe Harold's Pilgrimage", he describes the fallen of both armies ( or all three, perhaps), buried in mass graves, as being "in one red burial blent". Something about a "fatal tomb" might be acceptable, and not out of harmony.