Hmm. Ok, i made some more of boost only constant current drivers with this IC. Quite a few of them didn't work at all. With some it really was the capacitor, that was shorted, but with others, i actually managed to kill the regulator.
After replacing it, the circuit worked fine again.. But it was frustrating because of the sheer number of them, and because i had to do it fast.. So i have not even checked what happens to the Vfb, if a regulator is damaged like that.
In most cases, when i tested a driver with a damaged regulator on a dummy load, nothing happened.
But there was one case, where the output current depended on the input voltage.. This reminded me of your problem. You said your Vfb changes with input voltage.. Well i guess i did manage to kill one of them in the same way as you....
About yours... It can't be fine at under 3V input voltage, but not fine at over 3V but still under the Vf of load....
If it works properly, nothing happens when the input voltage is between 3V and Vf of load.. With the boost only version of the circuit, the input voltage has to be over 2.5V, but under the Vf of the load, or under 5.5V, whichever is lower.
Meaning, since the Vf of your load is 6.5V, the input voltage has to be between 2.5 and 5.5V, and the output current HAS to be the SAME, during this entire input voltage range! Oh, and sometime, they even work flawlessly down to 2V..
If the current changes with the input voltage, then either your regulator is damaged, or soldered bad, or there is something wrong with your circuit design..
Again, post pictures of your circuit please. With and without the components.
And just because the previous one was doing the same, doesn't mean it's not a damaged regulator. I've been working with electronics for 10 years, and yet i managed to kill many of them simply because i was in a rush.
With each one, i put it on a dummy load, set the input voltage to 3V, and measure the output current. Then i vary the input voltage with the fine adjust pot on my PSU (changes the voltage by 1V), to make sure the output current stays the same. But one time, i was looking at my DMM and grabbed the wrong pot and turned it... The voltage went to 16V! :
I don't remember what exactly happened to that one, because i was in such a rush. Maybe that one started varying the output with the input voltage.. Not sure.
But i do think your regulator is damaged. Soldering it for too long can also damage it. Or there really is something wrong with your circuit..