The Wikipedia article on the Nibelungenleid has an External Link (all the way at the bottom) to an audio recording in Middle High German that may give you a sense of the rhythm and metrical structure of the original that it seems Needler is trying to preserve.
The html version of Needler's 1904 text available on Project Gutenberg states in the preface that, "[his] apology for presenting this new English version of the Nibelungenlied is that none of those hitherto made has reproduced the metrical form of the original". However, Wikipedia lists an 1898 metrical translation by Alice Horton that may be more successful for your purposes. There is a link to a Google archive pdf version under the "English Translations" section at the bottom. (Both of these are free online in the public domain. I've been using them for comparison.)
Looking to Middle English is probably not useful to make sense of either the rhyme scheme or the meter. The best known ME scheme is the bob and wheel, which is completely different to the MHG poetic style. The alliterative structure and rhymes are likewise dissimilar.
From comparing excerpts in MHG, modern German, and modern English, it's clear where the rhyme scheme becomes difficult in translation. Here are the Needler and Horton versions of stanzas 70 and 83 that you mentioned:
Needler (lines 3 & 4 don't rhyme) (lines 1 & 2 slant rhyme)
Stern warriors stood there sorrowing, / —in tears was many a maid.
I ween their hearts erred nothing, / as sad forebodings said
That 'mongst their friends so many / thereby were doomed to die.
Good cause had they to sorrow / at last o'er all their misery.
Horton (lines 3 & 4 use slant rhyme)
Sad-hearted were the warriors, and many a maiden wept:
Doubtless their hearts forboded mischance for those who leapt
That day into their saddle, -- they dreamt these friends lay dead, --
They had good cause for mourning, in sooth there was much need!
Needler (lines 1 & 2 use slant rhyme)
What were the king's good pleasure, / asked Hagen grim in war.
"In the court within my castle / are warriors from afar,
And no one here doth know them: / if them thou e'er didst see
In any land far distant, / now shalt thou, Hagen, tell to me."
Horton (lines 1 & 2 use a different slant rhyme)
What the king wanted of him? first, Hagen sought to know.
"There are within my palace strange warriors, I trow,
Whom not a soul here knoweth; if thou didst them e'er see,
Declare it now, Sir Hagen, and tell the truth to me!"
The introductory sections of both authors discuss the difficulties of translation and which sacrifices each has made for various reasons. Comparing these two versions is quite interesting. I'm not fluent in modern German, but I understand enough of the pronunciation and syntax to understand the rhyme and meter. This has been a curious miniature research project.