Has anyone tried one of the Girard Perregaux "Presto" hand-held crystal press, or a similar one? The design looks like it would be resistant to flexing or getting out-of-square, but as I've never even heard anyone discuss this type, and no one seems to make a modern version, I wonder if it's one of those things that just didn't work that well and was consigned to the ash-heap of horological tool history.
Taking a closer look at your picture it could be the jewel is not sitting right as there appears to be a gap between the jewel edge and the chaton in the upper left quadrant in the circle. So if the jewel is sitting high at the lower left position (of the jewel) this would mean a gap and the oil migration to the upper right.
These Seikos (and Orients) don't need much power so this would equate with low mainspring power. 24hours sounds OK. I would wind it full and wear it for a day and see how much amplitude it has at the end of the day. Then leave it overnight and check it again in the morning.
If the autowind is efficient the reading at the end of the day (close to full wind) and in the morning (50% wind?) should not vary much.
Got a test I think would be interesting to try. Fully wind it and put it on the time grapher. Then with a piece of peg wood or something soft grip the teeth on the barrel and push it in the direction in which it unwinds with gradually increasing force. How would the rate change/line look as you're doing this?