Tile sheet with different sized tiles

I have a tile sheet of isometric tiles, where the tiles aren't all exactly the same size and aren't placed like tiles would be, neatly in rows and columns. For example, the "first" tile in the sheet is at coordinates 265, 1057 and is 132 pixels wide and 83 pixels tall. The next tile is at 265, 1452 and is 132 pixels wide and 99 pixels tall. Next to the sheet, I have an XML file which defines all the tile positions and sizes by their names so extracting them from the sheet is just like loading them as individual images.

Currently, Tiled wants all the tiles in the sheet to be the exact same size and be placed neatly in rows and columns in the sheet, which means I can't use my tile sheet in Tiled.

Would it be possible to add a way to read tile positions and sizes from some kind of file, such as an XML file like I currently have? It can be a proprietary Tiled file, following a Tiled format, it shouldn't be too hard converting between my XML and it. I would think it would work just like using a collection of images, but have the images come from a sheet, rather than individual files.

The issue names no files, tests, or entry points. Start by tracing how Tiled loads tilesets and collections of images, then compare that flow with the requested XML-defined positions and sizes; done means a non-grid tile sheet can be imported and used like a collection of individual images.