If you like the pick, and you still have money later, offer him less than his latest demand. You can still get him, but you have to be patient. For example, if you are planning to use the money on an IFA, but end up without an impact guy, go back to your pick and see if you can get him.
I had a very similar example to this and I really wanted the player. I was prepared to lose him and keep the Type D, while getting an impact IFA. When that didn't pan out, and I had money at the end of the season, I went back to the draft pick and offered what I had - greater than the 6.2M, but less than the 11M he was asking for. Finally, after numerous attempts offering the same money every time, the guy signed with me.
So you're not shut out - you actually have options at this point.