Updated the opening post with a video and a more detailed explanation.
I don't think this is directly related to the Plugin Delay Compensation problem, as the offset between audio and MIDI happens without any latency inducing plugins. Although this could indirectly be related:
Putting a few instances of linear phase EQ:s on the software synth (the video on the opening post) introduces offset between the hardware (audio) and software (MIDI) synths when monitoring the input.
I would expect them to play in sync with each other and the click, but with greater total latency. Meaning the click and audio track (no latency plugins) would be delayed by PDC to match the total latency of soft synth track. But this doesn't happen. PDC is enabled.
Still, the incoming MIDI note got recorded in the exact same position as without any latency plugins, but now it was clearly heard with a ~250 ms offset. And click and input audio were not PDCd. PDC is enabled for external MIDI sync also.
Here's a picture of the results:
Top track shows where the MIDI note got recorded.
2nd track shows whats was heard during monitoring: soft synth tone with 4 linear phase EQ plugins (left channel), gets delayd 'by a mile', but click and audio are not compensated.
3rd track shows playback of this recording: now PDC seems to work, and soft synth tone is where the MIDI note is (which is still wrong position however). And difference to what was monitored during recording is ~250 ms.
4th track shows where the incoming hardware synth audio got recorded, even though it was heard in sync with the click during the recording (2nd track, right channel).
It would seem that even a simple audio recording by playing in 'pocket' (early) through software monitoring latency would result in the recorded audio to being placed in the absolute early 'non-pocket' position, and not how it was heard in relation with the other tracks when monitoring.