I'd like to share with you, first, a legal definition of a strict constructionist I found on the Cornell Law Library website, since it seems as though that is how you view yourself. It states the following: "strict constructionists often look at the literal meaning of the words in question, OR, at their historical meaning at the time the law was written. Also referred to as "strict interpretation" or "original intent", because a person who follows the doctrine of strict construction of the Constitution tries to ascertain the 'intent of the framers' at the time the document was written by considering what the language they used meant at that time." Alexander Hamilton who actually was one of the framers or the Constitution, unlike Thomas Jefferson who was absent from the Constitutional Convention, writes in Federalist #78 how the term 'judicial power' is to be understood. He writes that "the constitution ought to be preferred to the statute, the intention of the people to the intention of their agents". He goes on to say that "the right of the courts to pronounce legislative acts void" (judicial review) does not "suppose a superiority of the judicial to the legislative power. It only supposes that the power of the people is superior to both; and that where the will of the legislature declared in its statutes, stands in opposition to that of the people declared in the constitution, the judges ought to be governed by the latter, rather than the former." It seems clear to me that this framer's intent was that the Court's judicial power should include the power of judicial review. Some historians explain that the only reason the term "judicIal review" is not expressly written into the constitution is due to the fact that some of the Anti-federalist legislatures would not have agreed to ratify had this wording been added. The term 'judicial power', which is expressly stated in the Constitution, according to what the language used meant at the time, included the power of judicial review.
The founders also intended for there to be a check by the judiciary on the other two branches. Without this authority, the Court would be too weak to survive. Since it has no authority to enforce its own rulings, or to make law, or possesses the power of the purse, it seems that this power to declare acts void places the Court on a more equal footing. Constitutionally, the lower courts are bound by this 'final word' and must follow the Court's decisions. Therefore, it seems impractical for the legislature to ignore this ruling and the executive to continue to enforce it. The legislature is obligated to at least remove the unconstitutional aspects of the bill in order that it may be properly executed and not continue to be a thorn with which the courts would continually have to face.
As to the power Congress has over the jurisdiction of the Court, the fact that Congress may make Exceptions to cases normally heard at the appellate level by allowing them to be heard under the Court's original jurisdiction doesn't allow them to strip the Court of its 'judicial power', only to determine if certain cases should go directly to the Court or be heard at a lower court first. I don't understand why you think all Congress has to do is pass some simple statute that would strip the Court of one of its judicial powers. Wouldn't that require an Amendment to the Constitution?
In addition, in spite of the fact that the Court has gotten it wrong at times as in Dred, Plessy and recently Citizen's United, when new evidence, and circumstances come to their attention, the Court eventually gets it right. I believe it is safe to say that the Court has clearly been right in its exercise of judicial review a large majority of the time. And thank God. Without this power of the Court, states would still have unjust laws that violate those fundamental guarantees spelled out in the 1st, 4th, 5th. 6th, and 8th Amendments. Thank God for substantive due process.