Would it be possible (or sensible) to use DEXseq for splicing QTL analysis? If, say, instead of a factor for experimental conditions, we used 0/1/2 as a numeric vector? Would DEXseq allow you to substitute a numeric vector for the condition, and would it treat this as a numeric vector instead of a factor?

In principle, it is possible to encode your genotypes as numeric vectors and run DEXSeq using this vector as your condition. A caveat of this approach is that you would have to run DEXSeq on every locus (or at least every time the levels of your condition change). If you have to many samples, this can become unfeasible, specially if you have many samples.