All of those avenues of research are already being explored.
What I would not do is say we absolutely just formed here as the earth cooled down and randomly happened and only do research based on that assumption.
I don't know of anyone who is saying that we "absolutely" formed here that way, nor is research being done "only" on that scenario.
However, it's no contradiction to also say that the best available evidence, and best available knowledge of the relevant fields, points towards natural abiogenesis. That conclusion could change overnight if new evidence or new knowledge ended up shifting the "best fit" theory towards some other conclusion. But at the moment, the admittedly incomplete evidence and knowledge (which in a real world are *never* "complete") indicates that abiogenesis is the best theory.
Science, in a nutshell, is all about honestly following the evidence where it leads (while looking for more), and accepting that even incomplete or sketchy evidence is a better indication of what's likely to be true than any guesses about what a fuller picture *might* indicate, or what we'd *prefer* to be true.
My gut instinct tells me life came from somewhere else than this planet, in whatever form but living,
"Gut instinct" being what you'd prefer to be true, or a guess about what might be. Why do you consider that a more reliable indicator than what an examination of the real world best indicates right now?
and there is nothing compelling enough in abiogenesis theory to change my gut instinct.
And just how familiar with abiogenesis theory are you, and how familiar are you with the known evidence?
That is not to say I could not change my thinking is some compelling evidence was discovered.
What if it already has, and you're not aware of it?
This is the dilemma when laymen adopt too much skepticism towards science, and refuse to believe some widely accepted theory (like evolution, *cough*) unless it can be explained to them in such great detail and so much evidence presented to them personally, that they are no longer able to think of any conceivable argument against it. It's especially a problem when they have preconceptions or pre-existing beliefs which would be challenged by the science.
Even professional scientists can't possibly personally verify every accepted scientific principle in every scientific discipline -- an entire lifetime would not be long enough to personally be shown and be convinced of every piece of evidence and every verification of every piece of the full body of scientific knowledge. So barring a damned good reason to question a particular conclusion in a particular discipline, the scientific individual provisionally accepts the established body of scientific knowledge, confident in the ability of the system to efficiently guard against the acceptance of nonsense to start with, and to eventually shake out the few bits of nonsense that manage to sneak in anyway.
And compared to any other system of discovering and accumulating reliable knowledge (or truth, if you will), science is lightyears ahead of whatever method is in second place. In short, the wise person accepts what science currently concludes on a topic (i.e., what the evidence indicates), and does not lightly cast it aside for what their "gut" thinks about it. For every person whose "gut" tells them "X", there's a person whose gut tells them the opposite. Intuition or feelings or even "common sense" are notoriously unreliable -- just look at liberals if you need an example.
Science is all about doing "reality checks" against the evidence, as a guard against getting stuck in the rut of what we'd *like* to believe.
But science is not a body of "gospel from on high" which cannot be questioned. On the contrary, being constantly questioned is what keeps it always self-correcting. HOWEVER, since established theories are built upon large foundations of evidence and verification (yes, including evolutionary theory and abiogenesis theory), it's ludicrous for someone to try to overthrow or tear down an existing theory without being armed with a great deal of knowledge about how and why the current theory has taken the form that it has, and what evidence and testing it rests upon.
This is why so many "amateur creationists" (and a lot of the allegedly professional ones) are so freaking annoying. They attack with little more than a firm feeling that the theory must be wrong somewhere, a small amount of knowledge about it (often wrong in fundamental ways, gleaned from poorly prepared creationist books or websites), and then smugly fire a popgun at a castle of theory while spouting something like, for example, "man couldn't have evolved from apes since there are still apes, all you scientists are real idiots for not realizing that, you're obviously just swallowing the Kool-aid of the anti-God conspiracy." Sigh.
The amount of hubris in such behavior is breathtaking.
As the old saying goes, "the first requirement for training a dog, is to know more than the dog". Likewise, anyone hoping to have a chance in hell of overthrowing a well-established field of science (including evolution), is going to have to make sure that they know the subject up, down, and sideways, which is not something they're going to learn from reading a popular book by Behe or Wells, or visiting a few creationist websites. Or by going with their gut.
[Thunderous applause!]