How can I mount a filesystem, mapping userids?

I can successfully mount an ext4 partition, the problem is that all the files on the partition are owned by the user with userid 1000. On one machine, my userid is 1000, but on another it’s 1010. My username is the same on both machines, but I realise that the filesystem stores userids, not usernames.

How do I find the offset of an ext4 filesystem?

I have a failing hard drive that is unable to write or read the first sectors of the disk. It just gives I/O errors and that is all there is. There are other areas on the disk that seem (mostly) fine.
I am trying to mount a partition (ext4) and see if I can access some files I would like to recover. Since the mount command supports an offset option, I should be able to mount the filesystem even though the partition table is unreadable and unwriteable. The problem is how to find the offset. None of the ext4 tools seems to have this particular feature.