In reply to:

Since you would need two things to throw together, "conjecture" has to be plural.

More on plural forms:

You would need at least two people to have a conversation (or two voices of some description), but conversation is singular.

I would use conjecture ordinarily with a singular verb unless it had somewhere been established in previous text that the conjectures had been reached independently of each other and that the 'conjecture' represented independent views. But this case would have had to have been clearly established in the preceding text. Even then, I don't like the sound of conjecture followed by a plural verb. However, I could train my ear to eventually accept that sound, if necessary.