I can think of two possible ways to do play-by-post games that require interjections, however both veer into becoming live-play due to the system rather than the methods:
Using a Google Drive and a shared Google Document, players could write their narratives and other players could see the changes being made in real time, this can allow them to interject via the in built comments, but this might still have the "a lot of retconning and backtracking" problem as it will just prompt users to go back and change what they wrote whenever a "Try A Different Way" phrase pops up.
Similarly to the Google Documents method, this allows players to see each other type in a live environment using a shared OneNote notebook, however, with OneNote's structure, each player could have their own text box in a sort of split-screen experience, this is more effective than the Google Document comments as a player would see the notice pop up as they are typing on the same screen rather than a possibly miss-able tab. If you choose this method, I would recommend copying over narrative and interjections into a sort of forum or document so you can see the amended history of the game and keep the OneNote notebook clean.
Both of these methods would, as mentioned before, be flawed due to the fact that they rely on players being active enough on the document to actually see each other typing so that they can interject, making it live-play with a text-based format. As mentioned by @lightcat in the comments of your question: "Best solution may be to "hack" the game", it's not exactly a play-by-post friendly system, but I can see it working with some decent homebrew. My methods are listed as a solution if you would like to stick to the rules as written.