If an allele exists currently at frequency X, and the selection pressure on it changes upwards, what should we expect? The frequency to increase. Of course it is possible for the frequency to decrease, and I made no comments on the variance of that expectation.

No. This doesn't follow. Consider for example an allele that is normally recessive and in the homozygous case is nearly lethal. Such an allele will generally be pushed to a very low frequency. The only way that such an allele stays at a substantial fraction of the population is if it is has a constant influx of new copies (For example Huntington's disease is sort of this way. The allele is dominant and extremely negative in that form, and is homozygous lethal, but Huntingon precursor alleles are constantly mutating into new cases of Huntington's and the specific biochem of the allele in question makes this much more likely). Now, if an allele has no impact in the heterozygous case. As the allele becomes extremely rare, the selection pressure will drop more and more to the point where it becomes negligible. Now, consider what happens if we discover a cure for this very rare disease that occurs in the homozygous case, or that we make it much easier to survive. What should we expect to happen to the frequency in the population? We should expect it to stay roughly constant, because there's no positive selection pressure.

In general, decreasing negative selection effects does not increase the frequency of an allele.