Such a broad interpretation of the Counting Clause would very likely be rejected by the Supreme Court. It is one thing to say that Congress has the right to count the votes, another to say that it has a right to dictate how electors shall actually vote.
Note that in the debate in Congress on whether to count the vote of a North Carolina Republican elector who had voted for Wallace in 1968, the majority of both Houses decided to count his vote--and one of the arguments used by the majority was that Congress simply had no constitutional power to disallow an electoral vote. See pp. 1693-4 of
http://scholarship.law.unc.edu/cgi/viewcontent.cgi?article=4003&context=nclr
Simply looking at the language of the Constitution, the counting function seems arithmetical and ministerial, not a license for Congress to decide how electors should vote. One might rebut this by citing the failure of Congress to accept the electoral votes cast for Horace Greeley after his death--but there it could simply be argued that Greeley was no longer a "person" within the meaning of the Constitution. What you are suggesting is an infinitely greater power, even a greater power than the power to reject faithless electors (a power that Congress has rejected). If Congress can do that, why can't it go further and say it will not accept any electoral vote not cast for the Democratic (or Republican) party?