You need to use the Unity Assets Viewer for that.
Open the resources.assets archive, search for the file "BtlEncountBgmMetaData.txt", export it, modify it and then re-import it.
Inside that file, there's a list of field IDs (so the Queen's Chamber in which you fight Beatrix is 1223) and for each field, a list of battles that can trigger in that field with the music ID of the battle ran. If a battle is missing there, the ambiant music doesn't stop when entering a battle.
So just find the field (1223), the battle (73) and put the correct music ID for it (117, "The Wavering Blade").
Here's a list of music IDs. I don't think that you can actually see it in Hades Workshop (only in the UAV when you open the music archive p0data62).
music033 -> A Place to Call Home (internal ID: 58)
music078 -> A Song from Her Memory (internal ID: 106)
music083 -> Aboard the Hilda Garde (internal ID: 112)
music012 -> Aloha De Chocobo (internal ID: 24)
music005 -> Amarant's Theme (internal ID: 2)
music117 -> Another Nightmare (internal ID: 45)
music122 -> Assault of the Silver Dragons (internal ID: 147)
music102 -> Awaking Song (internal ID: 77)
music070 -> Bahamut is Summoned (internal ID: 98)
music006 -> Battle (internal ID: 0)
music071 -> Before the Altar (internal ID: 99)
music043 -> Beyond the Twilight (internal ID: 67)
music054 -> Black Mage Village (internal ID: 82)
music024 -> Boss Battle (internal ID: 35)
music059 -> Bran Bal, the Soulless Village (internal ID: 87)
music114 -> Broken Spell, Healed Hearts (internal ID: 146)
music044 -> Burmecia (internal ID: 68)
music077 -> Chamber of a Thousand Faces (internal ID: 105)
music097 -> Cid's Theme (internal ID: 133)
music049 -> Cleyra Settlement (internal ID: 80)
music064 -> Cleyra's Trunk (internal ID: 92)
music062 -> Conde Petie (internal ID: 90)
music037 -> Court Jesters (internal ID: 53)
music087 -> Crystal World (internal ID: 121)
music093 -> Daguerreo, the Hermit's Library (internal ID: 129)
music003 -> Danger in the Forest (internal ID: 4)
music057 -> Dark City Treno (internal ID: 85)
music098 -> Dark Messenger (internal ID: 134)
music067 -> Desert Palace (internal ID: 96)
music069 -> Devil's Ambition (internal ID: 97)
music030 -> Distant Memory (internal ID: 59)
music121 -> Doga and Une (internal ID: 148)
music050 -> Eidolon Wall (internal ID: 81)
music060 -> Eiko's Theme (internal ID: 88)
music113 -> Esto Gaza (internal ID: 144)
music055 -> Eternal Harvest (internal ID: 83)
music014 -> Eye to Eye (internal ID: 20)
music038 -> Faerie Battle (internal ID: 61)
music101 -> Final Battle (internal ID: 71)
music013 -> Find the Princess (internal ID: 27)
music053 -> Fleeting Life (internal ID: 76)
music116 -> Foolproof Love Letter Scheme (internal ID: 141)
music048 -> Fossil Roo (internal ID: 79)
music011 -> Freya's Theme (internal ID: 32)
music001 -> Game Over (internal ID: 6)
music063 -> Gargan Roo (internal ID: 91)
music010 -> Garnet's Theme (internal ID: 29)
music105 -> Girl of Madain Sari (internal ID: 139)
music118 -> Guardians (internal ID: 72)
music082 -> Hunter's Chance (internal ID: 111)
music111 -> I Want to be Your Canary (internal ID: 145)
music031 -> Ice Cavern (internal ID: 60)
music080 -> Iifa, the Ancient Tree of Life (internal ID: 109)
music112 -> Inseparable Hearts (internal ID: 142)
music075 -> Ipsen's Castle (internal ID: 103)
music115 -> Kiss of Betrayal (internal ID: 41)
music066 -> Kuja's Theme (internal ID: 95)
music088 -> Light of Destiny (internal ID: 124)
music047 -> Lindblum (internal ID: 74)
music058 -> Look Back, See the Frog! (internal ID: 86)
music092 -> Master of Time (internal ID: 118)
music084 -> Melodies of Life (internal ID: 113)
music096 -> Memoria (internal ID: 132)
music046 -> Moogle's Theme (internal ID: 73)
music081 -> Mount Gulug (internal ID: 110)
music061 -> Mourning in the Sky (internal ID: 89)
music025 -> Oeilvert (internal ID: 36)
music027 -> Out of the Frying Pan (internal ID: 49)
music026 -> Outlaws (internal ID: 44)
music045 -> Over the Hill (internal ID: 69)
music056 -> Pandemonium (internal ID: 84)
music106 -> Peaceful City (internal ID: 138)
music120 -> Prelude (internal ID: 156)
music041 -> Prima Vista Orchestra (internal ID: 65)
music089 -> Protecting My Devotion (internal ID: 125)
music032 -> Qu's Marsh (internal ID: 57)
music009 -> Quina's Theme (internal ID: 15)
music036 -> RUN! (internal ID: 52)
music090 -> Roses of May (internal ID: 116)
music052 -> Rufus' Welcoming Ceremony (internal ID: 75)
music094 -> Ruins of Madain Sari (internal ID: 130)
music079 -> South Gate (internal ID: 108)
music110 -> Star-Crossed Lovers (internal ID: 143)
music039 -> Steiner's Delusion (internal ID: 62)
music007 -> Steiner's Theme (internal ID: 10)
music017 -> Swords of Fury (internal ID: 18)
music095 -> Terra (internal ID: 131)
music042 -> Tetra Master (internal ID: 66)
music109 -> The Black Waltz (internal ID: 140)
music020 -> The Evil Within (internal ID: 30)
music108 -> The Extraction (internal ID: 7)
music016 -> The Fateful Hour (internal ID: 17)
music073 -> The Four Mirrors (internal ID: 101)
music018 -> The Meeting (internal ID: 12)
music091 -> The Wavering Blade (internal ID: 117)
music021 -> Thy Warmth (internal ID: 33)
music022 -> Tragic Love (internal ID: 25)
music072 -> Ukulele de Chocobo (internal ID: 100)
music029 -> Unforgettable Silhouette (internal ID: 50)
music004 -> Unforgettable Sorrow (internal ID: 1)
music051 -> Unrequited Love (internal ID: 70)
music015 -> Vamo Alla Flamenco (internal ID: 22)
music000 -> Victory Fanfare (internal ID: 5)
music002 -> Village of Dali (internal ID: 3)
music008 -> Vivi's Theme (internal ID: 9)
music068 -> Wicked Melody (internal ID: 94)
music028 -> You're Not Alone (internal ID: 48)
music085 -> Zidane and Dagger's Song (internal ID: 115)
music023 -> Zidane's Theme (internal ID: 34)