Simpson makes brackets that can be attached with joist hanger nails that are NOT joist hangers; I have them on the ends of my stair stringers. Most likley the:
L/LS/GA Reinforcing and Skewable Angles
I suppose other companies make similar things, though to some extent SST is such a behemoth I don't know of any others in my local market. Anyway, if the ledger is carrying the bottom load, these will provide reenforcing for the attachment.
They also make flat reenforcing plates that could be attach across the splits to stabilize them, at least temporarily (which can be a few decades in house work, often enough...)
Not at all surprising to me that the 4x4 "mast" broke as you describe. The geometry of a zip line is such that the tension on the line is many times greater than the weight of the rider.
One secondary source suggests installing the cable such that the sag is 5% of the span. If this guideline is followed, the weight of the rider creates a pulling force at each cable support of 5 times the riders weight. The support also needs to take the load created by the cable itself, which is also a multiple of the weight of the cable.
Apparently the Association for Challenge Course Technology (ACCT) and the Professional Ropes Course Association (PRCA) both publish standards on zip line design and installation, which should be considered the authority on such matters.
DISCLAIMER Everything that follows is illustrative only, the above references should be consulted before building a zip line.
So now to attempt to answer your question: How many pounds of "pull" should a piece of 4x4 lumber hold, given a load applied 3 feet from the support point?
You've essentially got what's called a cantilever beam. In a cantilever beam you have both bending and shear stresses to consider, though in this case the bending stresses are the primary concern.
A #2 southern pine 4x4 post has a maximum allowable fiber stress of 850psi.
For a simple beam of square cross-section
Max bending stress = 6*M/(b^3)
where M is the bending moment (load in the cable (P) times the overhang of 36 inches)
and b is the length of a side of the square (3.5 inches for a 4x4)
Rearranging a bit to solve for the max "pull":
P=(b^3*max allowable stress)/(6*length of overhang)
P=(3.5in)^3*850psi/(6*36in)=168lb
So the post can withstand about 168 lb of pull from the cable (really it should be a little bit less when the shear forces are also considered).
But as I stated earlier, the tension in the cable can be around 5 times the weight of the person hanging from the zip line, so the max "safe" weight with this back-of-envelope calculation is only around 168lb/5=34lb, even before applying a typical factor-of-safety to the calculations to account for the dynamic nature of the load, and the fact that a person's (relative) safety depends on it.
So based on these calculations, even with just kids on the zip line, you were very near, if not exceeding the design load limits for your 4x4 post.
With a 3 foot overhang, a 4x4 post is nowhere near strong enough to safely support a zip line, even for kids.
Best Answer
I wouldn't be bolting the supports over the drywall. You will get movement back and forth from the bag and that movement will start to compact the drywall and eventually loosed the supports.
Think about installing a 4x4 between two joists with joist hangers. Then drill a hole through the 4x4 and install a 1/2" eye bolt and hold it in place with nuts and washers.