No, they do not fail to address your comment and therefore are not strawman arguments. Again, you explicitly state that your only exemptions would be for medical complications, not personal choice. Therefore you are advocating for the government to override the personal choice of individuals in a matter that is purely personal relating to whom it concerns. That isn't exactly a hallmark of a free society. Quite the opposite, in fact. It doesn't matter that you want it to be vetted more and guaranteed to be safe. While admirable, you're basically using that as a moral justification for the aforementioned stripping of freedom which forms the basis of your platform on this issue.
'If the virus mutates, what then?' you asked. Well, that depends on the mutation. If it follows the pattern of say, the common cold, and mutates in such a way that vaccination proves nigh-pointless while the overall lethality of the virus remains the same, and if further mutations seem likely, then what good would it be to produce new vaccines? I'd rather the resources of world governments be focused on other options, since producing a vaccine every year seems like a seriously inefficient usage of resources better devoted towards devising new ways to combat the spread at other points along the contact chain. If it mutated and became orders of magnitude more lethal, mirroring something like TB or Ebola, then we'd certainly need a more comprehensive revaluation of our strategy to combat the virus across the entirety of society (including massive and mandatory vaccination). As it stands though the virus is nowhere lethal enough to warrant such a response, which is right now reserved for extreme cases such as a smallpox bio-attack.
We've all had a tough year-and-a-half, pal. My advice is to take a page out of the British playbook; chin up, stiff upper lip, and soldier on. You're not alone in your suffering. We've all lost time, memories, and people to this pandemic. The difference between a year ago and now is that anyone who wishes can vaccinate themselves freely. By this point just about everyone who wants a shot has gotten one. What good then does it serve to impose vaccinations upon anyone else? The people who want to play it safe have done so, and those who would rather not (for whatever reason) will face the consequences if that is their fate.