I just made a quick test with one song and it worked fine for me (I have not tried SMP with EZKeys before)

Loaded the song into SMP
Exported MusicXML
Loaded MusicXML into MuseScore4
Exported partiture as midi
Dragged the midi into EZKeys2 chord line (only the chord name line, I didn't drag in the midi line)

It seems to work fine for that single file that I tested. All chords names and extensions loaded into the correct places in the time line the song had parts with several chords in a bar, and chords with various extensions.
I did not change any Keys. The song was in the correct key in SMP and was loaded with the correct key into EZK.

Maybe it works better if leaving the key cange to the last instans ie in EZKeys once the chords are loaded.

I just tested one song and that one worked fine for me.

EDIT:----
I only tested that the chord names were imported correctly (not the chord midi).
I did another test later it also worked fine but here I had misses in two places eg one bar with G-G/D-G/D-G/D was loaded as 4 G/D and similar on one other bar, but in overall the rest was correct and worked well and it was quite a complicated chord structure and chord types.
(I also tried to import the midi file to BIAB but that required a lot of editing, the amount seems to vary depending of the song. To import chords from SMP to BIAB from MusicXML via MuseSCore while waiting for a bug fix see posting above).

(I have reported the problems with loading MusicXML files into BIAB to PGMusic as a bug (assumed bug, BIAB only loading root names but not extensions) They can reproduce the problem and will have the developers look into it. If there are other problems with loading MusicXML into BIAB maybe it would be useful to notify them so they can fix it all in one go.)