Re: Ibanez SA220FMT
Welcome to Jemsite!
Here are a few things you might try. First, you said you installed locking tuners, but then said you use at least 2 or 3 windings. If you have locking tuners, you shouldn't have any more than one winding around the post. Just pull the string straight through the hole, yank on the string to get all the slack out, lock the tuner and tune it up. Having the extra windings around the post could cause some sting slippage.
Also, the Wilkinson VS100 will not fit -- the distance between the trem posts on the SAT30 tremelo is not the standard spacing. You would have to remove the old posts and drill new holes. That is a big operation.
Before you give up, I'd suggest that you try lubricating the nut grooves, the saddles (under the strings), and the contact area where the trem knife edges meet the trem posts. If it is available in Bahrain, you can try "Big Bend Nut Sauce" for this. If it's not available, you can use some other greasy, or silicon based lubricant like "ChapStick" (lip medicine). Some people prefer graphite (pencil lead) -- that works in the nut, but doesn't work so well for the trem posts.
Also, try loosening the strings and inspecting the knife edges. If they are chipped or worn looking, you may need to gently file them smooth again. Finally, the nuts on most Ibanez guitars are shipped from the factory cut for 009 gauge strings (009 to 042). If you changed the string gauge, the strings may be binding in the nut. In that case, you may need to have a tech inspect and recut the nut slots.
Even though you don't have an Edge or Floyd Rose style trem, you should read the stuff in the Ibanez Rules tech section about setting up the trem "flat" so that the knife edges are horizontal (perpendicular to the trem posts). That requires getting the springs adjusted so that they balance the string tension. If your trem does not appear to be more-or-less level, you should look into this.