WIP: Replace TSLint with ESLint

[andyleejordan]

Opening this draft PR to keep track of the work. I had started to resolve #2882, but the recommended migration method results in 3,150 problems, and it moves us to an already out-of-date version of ESLint. So after talking with @rjmholt and reviewing ESLint's FAQ I think we should redo this by moving natively to ESLint's recommended configuration (no TSLint migration, except for comment directives) and then allow ESLint to reformat the codebase.