this is a good starter to see what I'm on about:
www.google.com.au/maps/place/Coralview+Island+Resort/@-16.9229985,177.3803405,3a,75y,29.71h,71.35t/data=!3m5!1e1!3m3!1sui2DOWpu07wAAAQfCbpRrw!2e0!3e11!4m2!3m1!1s0x0000000000000000:0x8049673320b98bed

Hi Chris,

I 've been on 2 kiting trips to Fiji in the last 2 years during the same period you've looking at.

One at Sarfari Lodge - warren the owner is a member on this forum and I'm sure he can fill you in with all the details you are after. Kitepower Sydney & QLD also run trips to warrens.
I was lucky enough to have good wind the whole week and kited both in the bay on relatively flat water (for a bay) and trips out to an offshore reef which was amazing and kite back about 7 odd km to the lodge. All with boat support and staff well drilled in safely picking up you & your kite.

The other was with Moon Tours on Tevenuni. Again plenty of wind and kiting in a bay over shallow flats. I had a great time on both trips. Like all reef islands - the tide plays a big part of when and where you will be kiting each day. It's unavoidable that the kites end up with plenty of pin holes as everywhere is sharp - even sandy looking beaches - but nothing tape doesn't fix.

As far as somewhere budget minded to find wind in our off season - it's certainly worth serious consideration.