I'm not sure I fully understand the description of the issue. SII NH36 aka Seiko 4R36 day and date change works (as far as the visible change is concerned!) as following:
- at 22:00 the date starts to change
- at 24:00 the date change finishes
- at 00:00 the day starts to change from primary to secondary language
- at 00:40 or so the day switches to secondary language
- at 02:00 or so the day starts to change from the secondary to primary
- at 03:00 the day finishes.
Does yours behave like this and if not, what's different?
BTW, to adjust the entire time period in which the procedure happens is completely trivial, you don't need to to swap whole movement (??). A watchmaker simply needs to remove and reset the hands. In other words, if yours perhaps starts the whole procedure at 00:00 and finishes at 05:00, thus being 2 hours late, it just needs to have the hands reset.