I have a 99 that does the same thing, or did. I found out I was doing a couple things it didn't like. First was it didn't like being shot off the type of rest the OP showed, or even sandbags. If I hold the forend with my hand, then put the back of my hand on either type rest it shoots tighter groups. The second thing I was doing that made it look like I had too much drop at 200 was in trying to be more precise at 200 I found I was holding the gun tighter, and worse, putting a lot of cheek pressure on the buttstock. With no cheek pressure the drop between 100 and 200 is about 2/3 that with cheek pressure.
With 99s I've always found them particular off the bench, so I always try to shoot them free recoil, with the front rest almost at the receiver (as somebody else mentioned). Don't pull them into your shoulder, don't lay on them with your cheek, don't get a death grip on the forend, and don't rest the forend on anything remotely hard.
I have Marlins and Winchesters also, that are much easier to shoot off the bench. For some reason though, the 99s always end up going hunting while the Marlins and Winchester stay home...
