No one is saying that the Haitians were directly influenced by the Tainos, that is practically common knowledge since the whole island was under Spanish rule for practically 200 years before the French landed on Tortuga island. Plus, the encroachment of the French on the western fringes of the main island started after Governor Ovando had ordered the depopulation of the entire western and northern part of the island, moving practically the entire population within easy reach of Santo Domingo. This is why its expected not just for Taino influence to be greater in Dominican Republic than in Haiti.
But, what I'm saying is that whatever Taino influence, as small as it may be in some aspects of Haitian culture, probably arrived via the Dominican Republic, considering that the early Kompas musicians did borrowed some aspects from Dominican merengue. Furthermore, you yourself mention that Haitian music has some Cuban influence and guess what? There's Taino influence in Cuba too.
And last but not least, some Haitians that have been genetically tested are registering Taino DNA. Yes, they are very few Haitians with this DNA, especially compared to Dominicans and especially to Puerto Ricans; and yes, the DNA is practically negligible since none thus far has registered more than 1% (the figures I've see are usually around the 0.5%). But what this points to is that the depopulation of the western end of the island, despite being successful enough to allow the French to settle there with relative ease, was not 100%. Some people probably managed to escape the reach of the officials and hid in the mountains. Another possibility are runaway slaves (even in Jamaica, where Taino DNA is non-existent in most Jamaicans tested and they, along with the Haitians, are among the more African people on this side of the Atlantic; Jamaicans that descend from the maroons that hid in the Blue Mountains are registering some traces of Taino DNA), who would had hid in the mountains and there mated with whatever number of Tainos or mestizos or whatever they found there. If DNA is present, then some cultural aspects had to survive too. Yes, the DNA appears to be absent from most Haitians and the few that have it, its barely there; but, a similar situation could had happened with the Taino cultural influence. It may be few and far between and, in fact, ambiguous, but it could be there and easily confused for something else.
My point is that while Haitian culture is overwhelmingly African, this doesn't mean its 100% African. Some Taino influence, as small as it may be, has to had survived and could possibly, due to its ambiguity within such a heavy African influenced country, be confused for African origin when it may not be African.
Hence the case of the g?ira...
There are not many Taino musical instruments used today anywhere in the Greater Antilles, but especially in Cuba-DR-PR, which is where the Taino legacy is strongest of the major islands. But, the few instruments are clearly identified, have been studied, and its beyond a reasonable doubt that they are of Taino origin. That Haiti has the g?ira as one of its musical instruments in a region where such instrument exists and is known to be of Taino origin, should be reason enough to suspect that it too is of Taino origin. Who knows, it might be the only legacy of the Tainos in Haitian culture, but its a hypothesis that can't be so easily discarded.