Tachibanaya
たちばなや
Tachibanaya doesn't publish a shared-bath policy, but it runs two paid private open-air baths, 月の湯 (Moon Bath) and 星の湯 (Star Bath), ¥3,300 for 60 minutes, on Atsumi's own hot-spring water.
あつみ温泉源泉かけ流し。四季を感じ、名湯を愉しむ。
Best for: Two private open-air baths, ¥3,300 for 60 minutes, on Atsumi's own source water
The two private baths' own page doesn't separately restate flow-through vs. filtered treatment; the property-wide description confirms genuine source water for the inn.