The thickness of the chip on a broach is determined by the height difference between the teeth. Thinner shims will reduce the number of teeth actually cutting, but will not change chip load on the teeth that are cutting. A shim of 1/2 the normal thickness will cause the first half of the broach to pass thru the bore without cutting. BTDT
Along with some of the previous suggestions, when broaching a part this long, a hole larger than the keyway can be drilled at the midpoint to allow an exit for the chips. They may not eject automatically (or even willingly), but a blast of compressed air will help.
When doing the broaching, turn the part so the side of the broach is facing you. This will allow you to observe if the broach is going off vertical and digging in. This is always a good idea, but especially in brass with its tendency to grab the tool. If it starts to dig in, you must stop, push the bushing out, remove the broach and start again from the opposite side. Never push a broach backwards out of a hole. While there is not much danger in brass or aluminum, this can roll the cutting edge. Push the bushing out, then remove the broach.
These are some hard learned lessons, I've broken a few broaches.