I suggest that if you use a jumpdrive it will take everything near you with it. This has a lot of interesting applications. In addition to making it harder to escape from anything you want, it allows you to do things like jump loot around, jump mines into enemy bases, jump enemies into friendly bases, jump barricades around, etc.
I also suggest that you be able to control the distance you can jump. I am not sure of the best way to do this, but I think for short jumps you could have a key to hold down, with the "target" moving farther away from your ship at increasing speeds, and when you release the key you jump to where the target is. This is clumsy but I can't think of any other ways without using the mouse and precision jumping is important for most of the interesting applications.
Now you may have just noted I am suggesting making the jumpdrive MORE powerful.

First all, repeated use is harsher penalties.
A single jump of distances less than half a system or so ought to have no more penalties than now.
More jumps within a short time, though, ought to start first using more power.
Then your shield or device start to be affected - there is a chance of random device deactivation or shield damage at first and then items will start to lose enhancements or gain negative ones.
Eventually items will start to get damaged, or they just disappear.
There is a chance of items coming back out of your hold or disappearing altogether (although slight).
Perhaps very prolonged (ab)use could draw the attention of alien/outside influences.