Here's what I think happened - nothing concrete, but a "best fit" for both the sourced facts and unsourced rumours.
Shelagh Fraser's lines were recorded on-set, along with Phil Brown and Mark Hamill.
During post-production, Lucas decided he wasn't happy with her performance (possibly due to her accent). So sound mixer Derek Ball was sent to Fraser's house to record replacement dialogue, presumably with her putting on an American accent for the recording.
During this ADR session, several takes were recorded. One take was used on the initial Dolby Stereo and Dolby 6-track sound mixes.
Then to quote from here:
After completing the multi-channel versions, the soundtrack crew created another English-language mix, a monaural mix, to be included on prints destined for theatres not equipped with a stereophonic sound system and for versions prepared for ancillary markets.
With each subsequent mix, the filmmakers seized opportunities to revise and enhance selected portions of the soundtrack where they had felt rushed or shortchanged creatively, wished different choices had been made for a given scene, or simply selected a different take of a given line of dialogue. Sound designer Ben Burtt recalls: "Because we were always trying to make the film better and better and fix things that were not right, there was some 'sweetening' done; things like different Stormtrooper or C-3PO lines, additional sound effects, or some different ADR."
So the difference in the mono mix is simply because it uses a different take from the ADR session.
Although the mono mix was considered definitive at the time, it lost favour due to the rise in popularity of Dolby Surround on home video. Since early home video releases had the 35mm Dolby Stereo mix, which was also used as the base for the 1985 remix, and the 1993 remix was based on the 70mm 6-track, the alternative Beru voice became a rarity.