Using a little power-scaling math because simulation at this scale is difficult, and the rules break down at large scales anyway:
No, No island. At least not for Earth-typical conditions and continuous existence.
First, a free vortex is needed. But it needs to be physical and have room for Jamaica in the center, so we'll choose a Lamb-Oseen vortex which can get a stable center. Based on that you need a viscosity much much higher than water to get a center region larger than 1 meter. For water you'll have an edge velocity close to Γ/188.5 km. Γ is an integral that is larger at larger radial distances.
Assuming you could ignore the slowing effect of a central landmass, you still need additional extra input to keep the whole thing spinning against the losses from viscosity. Near the equator you can pull about another 1 meter/sec from the Coriolis effect at 50 km radius and Earth's Coriolis Parameter. As far as tidal forces and pressure forces, at Saltstraumen you have the strongest tidal forces on earth at 41 km/h yet they only create 10 meter whirlpools. If we increase that number by 300 km/h for some of the strongest thermal currents on Earth, the Katabatic wind). And then if we scale linearly, we could possible walk away with 83 meter diameter whirlpools.
If instead of instead of a singular whirlpool you can accept a chain of smaller ones then I don't think there is an effective limit as you just need more turbulence. The vorticity at high energies in a turbulence will create little whirlpools everywhere.
Yes, If you toss the island requirement then your 100 km region is very doable. The Great Red Spot can have several Earths fit inside it for example.
I can also see turbine-shaped mountain ranges from pole to pole that gradually smooth out. A rapidly spinning planet would have the water forced towards the poles from the mountains and the centrifugual force would tend to force the water towards the center. Circulation would form a whirlpool I would imagine. The setup balancing Roche limit, pressure, and centrifugal forces would be tricky to compute because calculating pressure would be hard.