The main problem with this bath seems to be the name: is it named after Eudoxia or Eudocia? The name of the bath is only attested in the Notitia.
EDITORS: check the 'substructure' in Bayülgen and Saner, 2024, p. 267-274 (Region VI, Substructure F 6/b, Plans 2 and 23). Would region VI be too far away from the Strategion in region V? Cf. Ibidem, 262-267 (Region V, 'Building with mosaic floor F6/a, Plan 2, Ill. 2). Note 300: original excavation publication by Duyuran 1960. Roman pottery sherds are dated to the middle of the 5th century the latest; a coin of Valens (r. 364-378) was found in the fill.