Negative percentages in a table of data
I don't necessarily know that I agree with your advisor's perspective, but the way you could do this is having "baseline" be 100%, and the changes between method A and method B being deviations from 100%.

So for example, rather than 5% and -7% you'd have 105% and 93%. This, to me, seems entirely stylistic in many cases, however may be consistent with things in your field. For example, relative risks in epidemiology implicitly use a scale somewhat like this.