"It seems more likely to me"
What if it's not a matter of either-or? He can feel guilt for leaving the dinosaur behind (which he establishes in the farewell speech in 1944) just as much as he can acknowledge his colossal screw up in the present. Shindo's death is ostensibly supposed to be the last hint of his misplaced faith in Godzilla, but I suggest it means more than just that.
Shindo achieved his goals when Godzilla defeated the Futurians. One would expect him to show tremendous joy. Instead, we get this:
This is the last we see of Shindo before his death. It's his reaction after King Ghidorah has been destroyed, after Wilson and Prof. Mazaki separately note that Godzilla will destroy Japan,
immediately after Dobashi criticizes Shindo's hubris. ("Is this your savior, Mr. Shindo?")
Would it make any dramatic sense for this shot to imply that he's now feeling guilty for having left the dinosaur alone to die on Lagos? Or would you concede that, by the placement of this shot in the narrative, the implication is that he's disturbed by something more recent?
Although obviously he couldn't have known Wilson's nor Dobashi's comments, that doesn't matter. What matters is that the viewer is aware of those comments and can use them to frame Shindo's expression. (A lesser script would have given us some exposition instead, perhaps by having Shindo voice his guilt.) The purpose of this shot in the film is at the very least to establish that Shindo's faith in his savior is now shaken. It's no great leap to assume that, because he now doubts his faith, he should also question his decisions and actions which led to the supercharging of Godzilla. After all, as has also been established, this Godzilla is far more powerful and destructive because it feasted on Shindo's sub.
Regarding his death scene, Shindo never expresses verbal guilt for leaving the dinosaur behind (this is only spoken by him at Lagos in 1944). He comments that he should have died on Lagos had it not been for the dinosaur. (He still can't accept that the dinosaur/Godzilla did not intentionally save him.) He notes that his survival allowed him to rebuild Japan (which includes his corrupt corporate empire), and he reflects on the irony that the dinosaur that saved him is now destroying his decades of work. That's all he (verbally) says in his final scene.
Perhaps you might get the idea that his last scene is supposed to show Shindo has lost touch with reality. I don't think so. Dobashi reminds him that Godzilla is heading his way, to which he replies "I know. This is how I want it. Let me have it my way." These are the words of a man who's accepted his failure and is preparing for his death. Japanese viewers probably would have understood this better than anyone else, what with the Japanese attitudes toward suicide in relation to great shame and failure (especially in business). So again, why should he feel this way? Because he helped kick off Godzilla's latest tour of destruction by using his own privately-owned nuclear weapons. But you're right, too, his suicide is not motivated by that alone.