Btrfs raid1 currently means "2 copies", even if you have 3+ devices. Btrfs is also capable of using different sized drives efficiently. Try creating a single volume raid5 with 3x 1TB and 3x 2TB. This is ~7TB usable (not including some space for fs metadata but does account for parity). Rebalance is not required when adding those 3x 2TB drives, they'll fairly immediately be put to use (the next time data chunks are allocated). And also no initial syncs when creating or adding drives.
Btrfs raid1 currently means "2 copies", even if you have 3+ devices. Btrfs is also capable of using different sized drives efficiently. Try creating a single volume raid5 with 3x 1TB and 3x 2TB. This is ~7TB usable (not including some space for fs metadata but does account for parity). Rebalance is not required when adding those 3x 2TB drives, they'll fairly immediately be put to use (the next time data chunks are allocated). And also no initial syncs when creating or adding drives.