I interpreted “lug-to-lug diameter no more than 39mm” literally as the case’s vertical/lug-to-lug length ≤39.0mm. That turns the list into a very small, mostly JDM dress-watch niche.
These are the models where the official page gives a vertical case size at or below 39mm, says sapphire, and the Japanese MSRP is under the converted $500 limit. Discounted street prices are shown where found.
The most rational tourist buy: slim, accurate, understated, and easy to find through Japanese retailers.
Same excellent dimensions/specs as SACM171, but warmer/dressier due to gold plating.
Variant with the same thin high-accuracy quartz architecture; check dial/case color in person.
Bracelet option and exactly on the 39.0mm limit. It will wear dressier/smaller than typical modern watches.
I treated Seiko’s Japanese “縦” measurement as the relevant lug-to-lug / tip-to-tip dimension, because it is the vertical case length. Anything over 39.0mm was excluded from the strict list even if the case diameter is 39mm or less.
Important: many watch brands publish case width but not lug-to-lug. I did not promote those into the strict list unless the vertical/lug-to-lug number was available from a source.
Under 39mm lug-to-lug plus sapphire is unusually restrictive. Citizen, Casio, Orient, Kuoe and Knot have plenty of small or Japan-interesting watches, but most either exceed 39mm tip-to-tip, do not publish lug-to-lug, use mineral/Hardlex, or exceed the price cap.
The Seiko Dolce 8J41 models are the standout: JDM-flavored, very thin, sapphire, high-accuracy quartz, and comfortably under budget.
These are worth knowing about because they will come up in Japanese watch-shopping rabbit holes, but they do not satisfy the literal filter.