I'm not against spending EXP, I just feel that Baleful Eclipse is the wrong thing to spend it on. Having high damage for it would be nice right now, but in most other situations it's overkill that doesn't improve our performance in a noticeable way.
So here's an alternative to what you suggested (Sunlight Scepter to 12 and Baleful Eclipse to 15) that works the same way but uses less EXP and makes the EXP that does get used go towards something that's more likely to be useful more often.
Purchase Sunlight Scepter: Spellslinger (350 EXP)
Upgrade Baleful Eclipse 10->11 (100 EXP)
This would make it so that using only a single action from each body, we can have Sun cast Scorching Sunlight at Brave Heart in order to use up her negation, and then in the same action follow up with Baleful Eclipse to KO Brave Heart.
If the Scorching Sunlight cast is the same as in today's update, then Baleful Eclipse performed in the same action as it, but immediately afterwards, behaves as follows.
Baleful Eclipse: 29856 Base Damage, No Dice, +100 Rebalanced Existence = 29,956 Total Damage
Brave Heart: 600 Base Resilience, 15594 Absorbing Aegis, Dice Negated, -11695 Juggernaut, -100 Standing Still = 4,248 Damage Reduction
25,708 Total End Damage.
Unwavering Shield (-4,211): 21,708 Total End Damage
Absorbing Aegis (90%): 2,149 Total End Damage
Brave Heart Health: 2250 - 2149 = 101
If Radiance can be added to Baleful Eclipse, that's more enough to beat her. If not, then you can either hope that being at 5% of her max HP makes Brave Heart unable to fight until she gets healed, hope that a situational modifier or will cover the last bit, or put one extra level into Baleful Eclipse (level 12).
Even if raising Baleful Eclipse to level 12 instead of 11, this uses 560 EXP, as opposed to your plan using 810 EXP.