How old was the yeast? Ultimately, it doesn't matter now, but this style and the Westy XII clones are all about the yeast. That high a FG is really unfortunate - mine finishes around 1.008. Re-pitching is questionable, unless you plan on making a starter, and even then, a partially-fermented beer is going to be missing the easy nutrients of fresh wort. At some point, it becomes a question of throwing good money after bad.
For an extract batch to finish that high, the yeast is probably toast and I have concerns it will not carbonate if you bottle condition. If you are kegging and force carbing, and you think it tastes fine, then by all means go for it.
If you plan on bottle-conditioning, I would think about either (a) pitching a fresh pack of dry yeast and seeing what happens, or (b) making a session-strength beer with a mild hop profile and using that as a starter and moving the partially-fermented quad onto that yeast cake.
This situation might be one place to use champagne yeast as a salvage technique. Champagne yeast won't do much to drop the gravity because wine yeast only handle simple sugars, but they do it really, really well and in rough conditions. If you pitch a packet, it will eat out any remaining sugars (leave it a couple of weeks), then it should have enough gumption to carbonate, even if the FG will remain a bit high.
K1 (V1116) might be a better choice here, since it can ferment maltroise (a slighly more complex sugar).
Danastar Belle Saison or Safbrew Abbaye might work as well and would be more in-line with Belgian-style yeasts, but again the partially-fermented wort is going to hurt their performance - how much, I do not know.
(BTW, my profile pic is the real thing in Belgium. The CSI recipe on the forums here is really close).