What is the direct object of "I imagined" in the context "as I imagined would be the case"? (i.e. I imagined what?)

'I imagined' does not have a direct object here, instead 'imagined' allows the clause that follows '___ would be the case' where there is a gap in the subject position. The whole construction headed by 'as' is usually a comparative adjunct in clause structure. E.g.

The team lost, as I imagined __ would be the case.

This is discussed in The Cambridge Grammar of the English Language p1147:

[28]

i [As I have already observed __ ,] no reason has yet been offered for this change.

ii The event was sponsored, [as __ is the fashion these days,] by a brewery.

iii He didn’t report the matter to the police [as you’d predicted __ ].

The comparative clauses functioning as complement to as are structurally incomplete in that the clausal complements which their verbs would have in main clauses are missing. They are recoverable from the matrix: in [28i], for example, what I have already observed is that no reason has yet been offered for this change. Similarly in [ii]: what is the fashion these days is for comparable events to be sponsored by a brewery. Example [iii] is ambiguous: what you’d predicted may be that he would report the matter to the police or that he wouldn’t.