I need to do this all the time, here's my method. It's easiest if you can snap to grid, but that's not essential. This particular method assumes no tempo changes are within the section to be moved; there are other options if tempo changes are involved.
1. Select all, place the Now time at the beginning of the section to be moved, and type S (split).
2. Select all, place the Now time at the end of the section to be moved, and type S (split).
3. Select all, and drag in the time ruler between the start and end times of the section to be moved. Now all the clips in that section are selected.
4. Right-click on any of the clips and choose "Create Selection Group from Selected Clips."
5. Go to Options and make sure "Select Track Envelopes with Clips" is selected.
You can now move the section as one entire block. Unless you ungroup the clips, you can keep moving it around as needed. If you need to include tempo changes that are within the section you're moving:
1. First go to Options and make sure "Select Track Envelopes with Clips" is selected, then follow steps 1-3 above. Step 4 is optional.
2. Select Cut Special or Copy Special, and check everything.
3. Place the Now time where you want the section to start.
4. Choose Paste Special, and make sure Advanced is enabled so you can select tempo changes and automation envelopes as elements to be pasted.
That should do it.