Does Flaming Sword of Rhuin actually add anything to the more powerful Ockham's Mindrazor when enchanted on a sword?
Obviously, I'm not the QM, but to comment on why I suggested the combo in the first place: there seems to be a disconnect between what the fandom thinks of when they think of Okkam's Mindrazor, and what the flavor text for the spell in the TT indicates. The fandom, as illustrated by somebody right here in this thread a few posts later, seems to think of the spell as enabling the caster to cut enemies with the power of their mind. But the text from the TT is:
The wizard summons phantasmal weapons for his allies that shred the folds of consciousness and reason. Victims of these mindrazors believe themselves slain, and so they die.
Which seems to indicate it's attacking the minds of enemies, not their bodies. Which in turn raises the obvious question of "wait, what about mindless enemies then?" The TT makes no provision for any difference in effects when attacking mindless enemies with the spell, but the flavor text seems to strongly suggest there should be.
You could rule that as "the flavor text is off base, and it actually works like the fandom thinks it does" or you could equally validly rule it as "the flavor text is correct, and the TT rules work like that to facilitate actual play and make it so that e.g. Skeletons aren't weirdly overpowered vs. Grey mages." So I suggested the combo to basically cover our bases: if it's ruled that Mindrazor inflicts mental damage, then it doesn't overlap with the Flaming Sword of Rhuin because that quite clearly does straight-up physical damage.
I have an alternate idea to your proposition. Flaming Sword of Rhuin is Moderately complicated... but guess what is also moderately complicated? Life Steal. It doesn't mess up our stealth, and if we manage to do it right we can solve our issue with our Healing item too. If our sword is vampiric, we can use it to heal while fighting.
I looked at Steal Life a few times, but ultimately leaned away from it. The reason being concerns over inadvertent
Dhar production. If
Shyish is pouring into our body as part of the return mechanism for Steal Life (i.e., first
Shyish affects the enemy to steal their life force, then
Shyish gives that energy to the caster) then if we have any other Wind-based magic active in our body it will mix and produce
Dhar. This is in-universe consistent, and also seems to be tacitly the major balancing factor preventing Mathilde from using her item slots to rock like 8 buffs at once from every Wind in the Colleges.
Now, you may be thinking, "but doesn't
Ghyran present exactly the same risks with the Seed?" And you would be correct, it absolutely does, and it actually in fact has in DL-canon done exactly that - it just did it after we got the Kragg Belt so it didn't ultimately make much of an impact. But using the Seed means that either:
a) We have assessed our need for healing, and made an executive determination that either there are no current risks of
Dhar or our need for healing is dire enough to justify the risk.
OR
b) We have been hurt so badly that the Seed auto-triggers, which absolutely meets the criterion of "our need for healing is dire enough to justify the risk." Because if the Seed auto-triggers, it's because we'd die without it.
However, there could be any number of instances where all of the following conditions were met at once:
1. We'd be at risk of
Dhar if another non-
Ulgu Wind enters Mathilde's body.
2. We don't have a sufficiently dire need for healing to justify that.
3. We still need to hit bad guys with our sword.
So that's why I ultimately decided against arguing for a Steal Life sword, as sexy as the idea sounds. With no Kragg Belt, it makes it way too possible/likely that we could find ourselves in a situation where we have to choose between not using our primary weapon or giving ourselves incurable
Dhar poisoning by using our primary weapon, for the sake of an effect we didn't even currently need.