Is God a Legislator or Executive? Or both?

Everything you have said seems to be a human looking at the matter from a human point of view. Scripture references, or any sources given to show where you got the ideas from, would be helpful. But if this is just your opinion, the danger of just getting opinionated answers arises. As a minimum, it would be necessary to define "natural laws" so that we are all on the same page. It may seem obvious to most people what "natural laws" are, but there was once a political party in Britain that used that phrase and boasted that some of their members could levitate from a crossed-legged sitting position, purely through meditation.

To answer your main question, "Is God a Legislator, or Executive, or both?" the Bible certainly shows him stating his laws which apply to humanity. That makes him a Legislator. The Bible also shows him carrying out his stated punishments on those who keep violating his laws - e.g. bringing about a global flood to deal with an incredibly wicked generation of people. He is also shown in the Bible blessing (rewarding) his covenant people when they keep his laws. He also is seen executing punishments on his covenant people when they persist in breaking the covenant (and the blessings and warnings of the consequences were written down alongside the laws they agreed to keep). That makes him an Executor. The answer to your main question then, is "He is both".

If, however, you refer to "the laws of physics" which humanity has only discovered comparatively recently, the entire material universe runs according to those laws of the Creator. This seems to be what you are thinking of when you ask if God is "pushing the stones around making it appear as if they follow that law".

Really, I can make no sense out of that question. If you refer to illusions in the material universe, then that question needs to go into an appropriate section, which isn't 'Christianity'.

You asked if "pre-Reformation theologians address this question". Did they even ask that question? If you can quote somewhere that suggests they did, more could be said.

First off, let me state that I'm answering in the assumption that "natural laws" means "laws of nature" (i.e. laws of science), i.e. not any sort of inherent moral laws. In other words, gravity, inertia, thermodynamics, and so forth.

I don't know of any pre-Reformation sources attempting to address this question. I'm not sure their understanding of science would have been sufficient to even know to ask such questions... so I'm just going to take a crack at what I think. Note that this is my own take, which may or may not be correct, but I'll give my reasons to help you think about this yourself.

Let's start with...

Option 3:

Natural laws co-exist alongside God, and any creation would need to follow them

What does the Bible say?

The Bible teaches that God is omnipotent. Certainly we know that God is not bound by natural law. But if God is not the source of natural law, what is? The above verses would seem to imply that God indeed is the source of natural law, and the fine tuning of said laws would seem to further indicate that they aren't an "accident".

One article goes so far as to state:

"[...] The steady will of Christ constitutes the law of the universe and makes it a cosmos instead of chaos, just as His will brought it into being in the beginning." (Theologian A.H. Strong)

All things are indebted for their existence to the continuous sustaining action of God exercised through his Son. Nothing exists of its own inherent power of being. Nothing in all creation stands or acts independently of the Lords will. The so-called laws of nature are nothing more than the physical expression of the steady will of Christ.

Thus, as we probably expected, it would seem that Option 3 is Not A Winner.

Options 1 and 2

1. God creates his creation, and natural laws, then His creation autonomously acts according to those laws.
2. God creates his creation, and natural laws, but He himself is the one — for lack of better words — pushing the stones around making it appear as if they follow that law.

Interestingly, our arguments against Option 3 seem to make a strong case for Option 2! But is that really the case? The God of Option 2 might as well be Randal Munroe; indeed, such a God might well be indistinguishable from an entity manually running a simulation.

Leaving aside the question of whether such a God is shuffling all the bits personally, or employing some sort of assistance, there are issues with this approach.

First, because it represents Creation in terms we can comprehend, it begs the question "where did God come from?". It also clashes with the idea that God is omniscient, knowing past, present, and future. The Bible repeatedly teaches that God is not bound by time as we are. This works when one understands that time itself is Created, and does not act on God the way it does on us. (Another problem with the Simulation Hypothesis is that it doesn't directly account for Free Will. Humans will cannot be the result of strictly material processes, or Free Will can't exist. Thus, humans must have some level of spiritual existence that is not wholly bound by the laws of nature.)

However, even if we've established that God exists outside of time, we've still shown that He is pushing all the bits around... right?

Well, hold on:

The image of God's Word having power is present throughout the Bible. He speaks, and it is accomplished. The picture we are given is not one of a micromanager, but one of a God whose power accomplishes His Will as easily as we might move an arm or a leg. We don't stop to think about our heart beating to pump oxygen-rich blood into the cells. We don't think about the complex mechanisms by which our cells turn food and air into energy, ultimately causing muscle fibers to contract. We just... move.

In the same way, my belief is that God isn't consciously directing every single atom. I believe He can do so, and I believe Creation would immediately cease to exist (or at least go catastrophically awry) if not for God's continued Power sustaining it, but I also believe the image of God having to actively and consciously "push all the bits around" Himself isn't accurate.

In other words, I would argue that the answer is neither Option 1 nor Option 2, but something in between, and possibly beyond our comprehension.