"Can I rebuild the partition table around the existing file structure?"
Yes, but there is a better way.
"Will writing a new partition table effectively format the drive?"
No. But if you change partition sizes while doing so then you will be forced to format the affected partitions.
I suggest that you copy everything to a backup. Then completely rebuild the partition table from scratch, format every partition, and restore the backups.
Be prepared. Create a LifeBoat CD.