It’s a little trickier in a couple of places for yours, but the “stop advancing the lyrics popover a note early and then lengthen the extender line after closing the popover” trick does work in your project.
In bar 23, you could cut the tie first, then advance to the last note in bar 22, press Esc, select the lyric, press Shift-Alt-Right arrow to lengthen it to the first note in b23, then retie. It seems the lyric has to have a bit of extender line in order to lengthen it, so in places where the lyric spans already more than one note before the last note (e.g. b25, there’s 3 notes before the last tied note) stopping (pressing Esc) when the popover is on the last note (and not advanced past it) works fine.
Or, just shorten the lyrics/extender lines that have already been advanced and have split the multi-bar rest: e.g. for the last lyric in b25, set your rhythmic grid to quarter notes, select “feel”, then press Shift-Alt-Left arrow 7 times to retract the extender line to the first note in b26 (i.e. the last note in the sung phrase).
(On a side note, if you apply the playback template “Silence” before sharing your projects, their file size will be much smaller.)