I think it's a little too dismissive to assume that "the dwarves killed themselves because Kagrenac was too proud to bother letting an intern check his math." It's not like he came up with this plan overnight, this was the long-term goal of their entire society and philosophy, and what their whole history as a people were leading up to doing.
If there was any flaw in their actions, it was in the whole of their philosophy to start with, but there is, again, no evidence that they actually failed at anything, and actually achieved their own form of transcendence (or should I use a different term... "Unnascendence?") The Dwemer are, functionally speaking, the Thalmor, but actually intelligent enough to know what they were doing, and having a proper chance of achieving it. They just didn't take the rest of the world with them.
You're right that there's no damning evidence that they failed, and I can actually make a fairly decent argument that they succeeded (which is why I say my article needs an addendum).
As for Kagrenac, it's not a matter of too little planning or not doublechecking his work, it's a matter of being forced to act before he was ready, and being forced to act in a panic.
Imagine if you were taking a test and expected to have an hour to take it, but then thirty minutes in the teacher told you you have two-minutes to finish - even if you had planned perfectly for an hour test and knew the answers do you think you'd still pass after that stunt had been pulled?
Kagrenac wasn't expecting to have to turn in his test when he did.
If anyone did too little research, it's the Tribunal. They either set their sights too low or did think things far enough through, and only achieved a demi-godhood. For all Vivec's desperate posturing as some sort of philosopher king to gain some fragment of respect, he didn't even achieve as much as Tiber Septim did.
Neither got higher than CHIM.
The Tribunal achieved what they set out to, they usurped their anticipations and ruled as god-kings for almost the entirety of history up-to-date; then Vivec took it a step further with CHIM and Seht possibly made literal truth his city being called "Sotha Sil".
The Tribunal were powerful enough to achieve what we've only seen Akatosh himself manage to date.