I'm going to rearrange the order of your questions a little:
Do you not think it important to weaken the power of money, special interests and political parties and the fostering of bad faith dishonest politics that is simply expedient and benefits the politician at the expense of the people?
My answer to this group of questions is an unequivocal yes.
That being said, sometimes a solution that may fix or eliminate one problem may create other, unintended or unforeseen problems(or even foreseen with careful consideration).
If sortition were to solve the above (which I'm not saying it will), I believe it would create other weakness that may even be worse (in my inadequately informed, non-professional opinion).
If you were selected, would you do your best?
In my experience, well-meaning people can be naïve, inadequately informed, not have the capacity to comprehend certain complex problems, have bias, overly rely on the expertise of others without sufficient background or understanding to evaluate the product of a presented expert, or to evaluate conflicting advice from multiple "experts". In addition, not everyone has the personality to manage people or creativity with which to find novel and efficient solutions to problems.
In regards to myself, I would attempt to do my best, and compared to the population as a whole I think I would do a better job than most, but there are those who would be a hundred times better than me at governing, managing, and solving political problems. Given the size of the population, that means there are plenty of people who are more suited to governing than myself, no matter how just and earnest I might be.
How many current politicians do you think qualify as both honest and having superior competence?
I'll take this question as rhetorical as I have no way to give a reasonable or informed answer. Even a politician who today appears squeaky clean publicly my simply be a politician who's dishonesty is yet to be discovered.
What I find interesting in this question is that there is almost a subtle assertion that it will have to be either/or. We can have honest politicians but of only average, functional competency, or we can have superior competence but a high probability of dishonesty.
It is my opinion that an honest, yet statistically person would be as harmful as a corrupt above average person in any high level government position.
How many current politicians would you happily replace with a random member of society (perhaps a bank manager, or an electrician or a doctor or a social worker)?
Yes, there are those politicians who glaringly stand out as ones we would happily replace with literally anyone else, but in seriousness, I would always much prefer they be replaced by someone with superior ability and who shares my values.
What reforms would you implement instead? (surely you can't think the status quo is desirable)
I am not a political scientist, nor do I have a hobby interest in the subject, so it would take some research and more than a bit of thought to give any kind of informed answer to this question.
Given that disclaimer, I see social systems as evolving, ever changing, and as such, see changes to the structure and rules of society as inevitable and necessary over time. So no, I am not for maintaining the status quo or inclined to conserve or preserve historical tradition simply for traditions sake.
It would seem to me that the most effective starting point would be to add some refinement to the Constitution. This is terribly difficult to do, by design, and in reality, given that whole states are polar opposite in goals and temperament from each other, no effective Constitutional amendments are likely.
As I mentioned in an earlier post, I speculate that election reforms that enhances the voice of the political middle and attenuates political extremes may be helpful, but given the strength of the current two-party system in the US, I see that kind of reform as quite the uphill battle.
The reality is, things may have to get much worse before meaningful reforms can be made.
As a last note on sortition and the expectation of candidate qualifications, it might be useful to relate the practice and endeavor of politics to other professional pursuits. Doctors, lawyers, engineers, the sciences, and professional academia all have long and rigorous training pipelines that are designed to ensure high competence and suitability in those that ultimately complete their respective program, and not all that attempt will complete.
Now I'm not suggesting that only those with a PhD in Political Science and Governance should be eligible for consideration to elective office, rather, I am suggesting that in our current system of campaigning and running for office, there is a public vetting process in which a candidate must demonstrate their qualifications and level of competency in an environment in which they are in competition with other candidate under the same scrutiny. Sortition as you have described would eliminate this process of evaluation and verification, leaving us with essentially no standards.
I can't imagine you would want those who are to be doctors or engineers to be selected by lottery from the population as a whole. Why then would you entertain less professionalism in prospective politicians?