The 1837 edition replaced the standard biblical “thou wouldst” with “thou wouldest”. This edition occasionally changed other cases of wouldst and shouldst to wouldest and shouldest:
Joseph Smith marked none of these changes in the printer’s manuscript (in his editing for the 1837 edition). And the clear majority of instances of shouldst and wouldst were left unchanged in the 1837 edition (13 other cases). So these few cases where the inflectional ending -st was replaced by -est were apparently due to a tendency (perhaps unconscious) on the part of the 1837 typesetter. Of course, in all these cases, the earliest reading will be maintained in the critical text. For a complete listing of shouldst and wouldst, see the discussion under 1 Nephi 20:5.
Summary: Follow the earliest textual sources in determining whether should and would should take the inflectional ending -st or -est when the subject pronoun is thou.