It left each, in some measure, dependent upon the others, as it left to each power to exercise, in some respects, functions in their nature executive, legislative and judicial. Thus, for example, the President does participate in the legislative process in several ways, most obviously through vetoing or signing a bill into law. The lack of an absolute and readily ascertainable line between the legislative and executive functions should not be viewed as a flaw in the constitutional design. Rather, the Founders anticipated that both the executive branch and the legislative branch may seek to invade the powers of the other branch, and the resulting struggle between the branches could be used, through the separation of powers, to guarantee liberty. You discuss the option for Congress to require the President, when invoking statutory authority to issue an executive order, to submit his proposal to Congress for review.
Presidents are likely to resist any attempts to limit their powers.
As noted above, that resistance was anticipated by the Framers and built into the constitutional plan. Nonetheless, a President could be led to agree to such a change, either in the interests of good governance, or as part of some larger political compromise with Congress. There are many ways to structure such a change. In the context of executive orders specifically, Congress has not done an effective job of protecting its interests. There are many reasons for that, including the increased scope of the duties assigned by Congress to the executive branch, which inevitably reduces congressional oversight over any particular program.