This is to do with the way FS handles winds. There are several layers, with a jump (not smoothed) between them.
Several possible solutions:
1. (Unrealistic) Fly at less than 250 kts, to create more of a buffer.
2. (Expensive) Pay for FSUIPC, which has a wind smoothing option. Unfortunately, if the wind change is sufficient, then pulling the nose up to maintain airspeed could mean that you exceed 4500 fpm and get a penalty that way. You can fix this by adjusting the maximum wind change rate in FSUIPC.
3. (Clunky) Use the wind smoothing function of IvAp. Even if you fly offline, run the client and the wind smoothing still works (at least I seem to remember it does). In the IvAp Configuration, turn on wind smoothing. Not as advanced as the FSUIPC implementation but it does the job. This approach also suffers from the Rate Of Climb problems above.
It seems there is not a free perfect way to overcame the jumps between wind layers. If you have the money, pay for FSUIPC and a lot of problems go away. If you don't, I recommend using IvAp (I do) and it does help quite a lot, even though it is not advanced like the FSUIPC version.