Importing tracks I record in a project with the same settings and BPM don't line up

I have an Ableton project that has several guitar, bass and vocal tracks and a drum track with EZDrummer on it.

I needed to record some additional guitar parts and in the main project I was getting too much latency for it to work.

I saved a mp3 of the track and opened a new Ableton project with the same settings and loaded the mp3 and recorded the parts.

Same BPM in both.

When I try to import the tracks back to the main project they are not synced. The BPM seems fine, there isn't drift as far as I can tell, but they start slightly off beat.

The tracks were set to start at the beginning of the track with no delay.

When I import the tracks they line up with themselves, but not with the tracks in the project.

If I import the mp3 from the guitar project it doesn't line up either, if I just load it now it also doesn't line up either, but it did before as I had loaded it to make sure it worked, but now the one that I load directly onto  track is out of beat with the one that I had imported directly onto track a few days ago.

I don’t have warp on and am baffled as to what is going on.