This is an answer to an attempt at understanding a previous version of the question, and is no longer relevant to the latest question.
Your question is: What happens when you use a simulating halt decider and (...)?
The answer is: You can't. The question has a faulty premise. A simulating halt decider does not exist, so there is no meaningful answer to the question.
I'll highlight your definition. You propose the following definition:
A simulating (at least partial) halt decider H is a UTM that has been adapted to decide whether or not its input halts. It does this by simulating its input and examining the behavior of this simulated input.
(I presume this should be interpreted as saying that, to count as a simulating halt decider, the UTM must always correctly decide whether or not its input halts, for all possible inputs.)
The problem is: there does not exist any UTM that successfully acts as a simulating halt decider on all inputs.
You can add all the conditions and requirements you want to a definition. The definition remains valid. But there is no guarantee that there exists any object that meets the conditions of the definition. That has to be separately verified.
It sounds like you think that there does exist such a UTM that would qualify as a simulating halt decider. However, your intuition is faulty. I know it's easy to identify some patterns that, if they arise during execution, allow us to determine whether the input will halt. However, those patterns will never be comprehensive. No matter how many patterns you write down, there will always be some inputs that aren't handled by any of those patterns.
Those of us who have studied complexity theory already know this, because there is a theorem that proves it. High-level statements such as "Certain patterns of behavior such as infinite loops and infinite recursion can be recognized." is not likely to be effective at persuading anyone to the contrary, because we know there are also other kinds of behavior that won't be recognized; yet such language is too vague and imprecise to allow us to give you specific examples to help you see that fact concretely.
If you'd like to pump your intuition, you can find some examples of programs where no one knows whether they halt or not: What are the simplest examples of programs that we do not know whether they terminate?, What are very short programs with unknown halting status?. If you study them, perhaps it will give you a better sense why these programs might fail to halt (they might run forever) without ever entering any loop, or even matching "pattern" that you can write down. (More specifically, for any pattern or list of patterns you have in mind, there might be some input that fails to halt but doesn't match any of those patterns.)
If you want an analogy, I find your assertions to come off (to me) as similar to the following made-up conversation:
Polly: Let's define an "awesome circle" to be a circle whose radius $r$ and circumference $C$ satisfy the relationship $C=8r+1$. What would happen if we replaced the 4 tires on my car with objects that have an "awesome circle" shape?
Conan: You can't. No such object exists. The question is meaningless.
Polly: Sure, but assume $H$ is an awesome circle, and I put it on my car. What happens?
Conan: You can't. $H$ doesn't exist. The assumption is false.
Polly: But my $H$ is defined to be awesome. An awesome circle is one that has been adapted so that $C=8r+1$.
Conan: You can't. You can't adapt a circle that way.
Polly: I have superior knowledge of round shapes. Anyone with my experience with round shapes would see immediately how to adapt a circle in that way.
I hope you can see how this exchange is a bit absurd and Conan would tire of it quickly and not have any interest in continuing the conversation. Of course, if Conan knows some mathematics, then he immediately knows that all circles satisfy the relationship $C=2\pi r$; since there is no solution to the system of equations $C=2 \pi r$, $C=8r+1$ with $r \ge 0$, any mathematician would immediately know that no "awesome circle" can exist, so there is not much point in continuing such a conversation.
This is how your attempts to address this topic come off to me. Your assertions remind me of Polly's assertions (Polly's awesome circle = your simulating halt decider; Conan = any computer scientist who has studied decidability). Hopefully this helps you better understand the reactions you are getting and use it to help you focus your future studies.