Some tables may be trickier to recite than others, e.g. when cells have different size (spanning over multiple columns etc.). Should column title be recited before each cell content?

I did a quick hack just allowing tables to be segmented and splitting segments on th and td elements. It seems that reading "simple" tables, i.e. no rowspans, colspans or other things that mess up the layout, works fine. It can read left to right, top to bottom (LTR text). Highlighting is non too happy so I had to disable it to work.