A steak to stuff?

One of my favorite summer grill dishes involves filet mignon stuffed with a mix of lobster and habanero or jalapeno infused cheese, with a beurre blanc.

The problem that I've been encountering lies with the filets that I've been buying from the Paulina Meat Market. They're rolled and tied, and it's not really feasible to make a decent sized pocket in them. Even with just a small pocket, the inevitably break apart on the grill.

Is there a cut that would be better suited for this variety of abuse? Perhaps some treatment that might prove to make the steaks a bit more resiliant? I'm just fishing for ideas, as the last attempt ended with 8 steaks instead of the four we started with.

What about rolling a steak around the filling, and tying?
Flank or round are typical for rolling, but tenderloin would work, as long as you were spending the bux on filet.

What about butterflying a tenderloin, stuffing, and rolling it up.

Another technique is to poke a hole through the tenderloin lengthwise, starting the cut from both ends with a boning knife and continuing the boring out with a sharpening steel. You can then pipe your stuffing through with an open ended pastry bag.

You might also consider making your stuffing and asking one of Paulina's butchers to do the grunt work for you. They made me some custom marinated, rolled, and tied boneless skin on turket breast rolls last year.