The process may be unconstitutional, but it's not unconstitutional for the reason you cite. You're leaving out two sentences from the paragraph you partially quote. The "But in all such Cases", refers directly and solely to cases where Congress is overruling a Presidential Veto.
I'm not sure who started this Art I, Sec 7 business, but it's insanely silly. For you to be accurate, every voice taken to pass legislation in either bicameral body, has been unconstitutional. If that's true, surely you can point to at least one case where such legislation passed by voice vote has been held to be unconstitutional, right. Can you even point to a single case that was brought, or that was granted cert based on your premise?
The Founder included in Art 5, the following paragraph...
"Each House shall keep a Journal of its Proceedings, and from time to time publish the same, excepting such Parts as may in their Judgment require Secrecy; and the Yeas and Nays of the Members of either House on any question shall, at the Desire of one fifth of those Present, be entered on the Journal."
Why would the Framers include this provision in Sec 5, only to demand that ALL votes be recorded in Section 7? Does that make any logical sense to you? It certainly doesn't to any Constitutional scholar that has ever actually studied the Constitution.
Thank you for the reply... This was exactly the reason for my post, to challenge my logic, which I now see is flawed on the Yea/Nay point. I regret the error, but I’m glad to have a better picture of the constitutional grounds. What is your interpretation as to my other argument, that reconciliation is restricted to modification of existing law, and therefore it can’t be used on the healthcare bill unless and until the passed bill is presented to, and signed by, the President?