For the specific task of copying selected MIDI clips from one project to another, preserving start times, and leaving behind unwanted events and track parameters, I would suggest something like this:
- Open both projects.
- Create the target MIDI/Instrument tracks in your new project (one for each track you will copy)
- Ctrl+tab to the source project.
- Select the tracks you want by sweeping and/or Ctrl+clicking track numbers.
- Ctrl+A to Select All.
- Edit > Select by filter, uncheck any data types you don't want and OK.
- Ctrl+tab back to the new project.
- Select the first target track, set Now time to 1:01:000, and Ctrl+V to paste.