Can I implement this in opentype: an overbar if a "t" is in a word

I'm prototyping a cursive font where, at least on paper, any word with a "t" in it has the crossbar on the t extended to the left and right over letters as long as this fits; verticals in h, l, d, etc. will cut off the bar, so something like:

becomes something like:

I'm not entirely sure how to implement this, though. I was thinking of using many-to-many GSUB rules based on glyph classes, but no matter how I look at it, it turns into needing recursive GSUB behaviour...

1) t [low] ->[t with bar that continues right] [low with left-connecting overbar]