Except SEELE wouldn't have needed three of their deepest cover agents to just kill Rei, getting to the Reiquarium on the other hand....
Taking Stryp's Insightful tag on that comment as confirmation, so new theory.
In canon, when Ritsuko throws the switch on Destrudo Release, we see a list on the tablet in her hand of Reis being affected. It starts with Rei-4, meaning Ritsuko didn't include Reis who were dead or active at the time. This makes sense: there was no point in including the dead Reis, and it wouldn't do to kill an active pilot.
The SEELE operatives, by contrast, just threw the switch on
all of the Reis, including the active one. It's unclear whether they actually intended to do this last: they were working on a beyond-top-secret system without proper documentation and time, and might nor have known how to make the necesssary adjustments.
Getting into personal theories on canon, I think Destrudo Release is exactly what it says on the tin: a crude but powerful shot of raw human death-drive (as named by Sigmund Freud). The Rei clones, lacking souls of their own, would have no defense against this, and simply die in the quickest and moat expedient method available to them: collapsing into LCL.
Gendo and Ritsuko realized, of course, that this was a critical weakness in their system. Rei could be replaced if killed, but what if she and the clones were all killed at once? Destrudo Release was one of the few things that could do that, and this put their plan in jeopardy. Precautions would have to be taken. So they designed a pharmaceutical cocktail, including extremely high doses of antidepressants...