The difference between the high prevalence of cancer in humans as a consequence of longer lifespan and menopause occurring due to the failure of the reproductive system does not at all seem clear.
High prevalence of cancer is the result of changes in the probability of cancer occurring during a person's lifetime. This is a failure of a biological process in cell regulation. As a person ages their chances of getting cancer increase with each year. So mathematically, an older person is more likely to get cancer, but will not necessarily get it.
Menopause does not occur as a failure of the reproductive system, it is a natural part of the reproductive system. The chances of menopause occurring do not change linearly with age. Instead, a biological process governs its onset, and it will generally occur between the ages of 40 years and 60 years.
Are you saying that just because not every human gets cancer (versus literally every human female experiencing menopause), that's a significant difference?
Yes.
Again, cancer is an event based on a statistical probability, not a specific biological process that will occur in every human. Menopause is a biological event that occurs as a natural part of the female reproductive anatomy. To help you understand that, menopause does not occur when a female human runs out of eggs, it is not a failure, it is as natural as menarche.
If humans universally didn't live past 40-50 for the majority of our existence, and have only experienced longer lifespans for the past few hundred or thousand years, the argument for it being a consequence seems much more reliable (and a lot less of a 'just-so' story) than menopause being an adaptation.
Your premise here is flawed. You are confusing the measure of longevity with the measure life expectancy at birth. Life expectancy is an estimate of how much longer a person will live from a given age, so it changes with age. Death of young individuals that have not yet reached the age of reproduction was significantly greater in the past. This puts a significant skew on the measure called 'life expectancy at birth'. Because of that skew, it is not very useful in making any good evolutionary argument about adult human life-history. Instead, you should look at life expectancy at sexual maturity (scroll to first paragraph) for historically informative longevity.
There is no well accepted argument for menopause being a consequence of aging.
The evolution of menopause is a long standing open question among evolutionary biologists. It has been well studied for decades. It leaves no real question about a failure. It poses a problem because 'fitness' describes only reproductive success. We would predict that reproductive success would be maximized by continuing to reproduce throughout the life-time of the adult female. But this is not the case. Instead, the adult female ceases reproductive effort on the creation of new offspring. The Grandmother Hypothesis was the first adaptive explanation for the evolution of menopause. It is the most famous hypothesized solution to the quandary.
it seems reasonable to assume that that percentage would increase if lifespan increased
Yes, but only as a probability. At some point the lifespan would be long enough that the probability a person will get cancer in his life-time would get very near to 100%. But the probability that a teenager gets cancer will not change. With menopause, if you increased the lifespan of the female ad infinitum, it would have no direct effect on menopause since the increase in lifespan would be totally post-reproductive.