Scribe 2 of 𝓟 initially wrote this passage as “let us repent and not harden our hearts”, the word order that we would expect in modern English. But scribe 2 immediately corrected the word order by erasing not harden and overwriting it with harden not. Oliver Cowdery, when he proofed 𝓟 against 𝓞, rewrote the correct harden not, first crossing out scribe 2’s harden not and then supralinearly inserting it. It is quite clear from both corrections that 𝓞 read “let us repent and harden not our hearts”. Moreover, the original text has nine other instances of “harden not”, five of which are conjoined to a preceding predicate:
Notice that the first two examples listed above also occur in Alma 12, only a few verses earlier. The critical text will maintain the corrected word order here in Alma 12:37.
David Calabro (personal communication) reminds me that Alma 12–13 also contains many phrases that parallel the King James language in the epistle to the Hebrews, including two uses of the phrase “harden not your hearts” in conjunction with a reference to provoking the Lord:
Thus the reading “harden not our hearts that we provoke not the Lord our God” in Alma 12:37 is undoubtedly correct.
Summary: Maintain in Alma 12:37 the corrected word order in 𝓟: “let us repent and harden not our hearts”.