A: This is actually a very good question and it touches on a few things we hear about fairly frequently from other customers. Since there are actually a few different questions buried in there, I'll do my best to break it down and offer some insight on each individual part—hopefully without missing any important details!
First things first, your cross strings are broken, but your mains are intact, so can you remove the cross strings and leave the mains? Technically the answer is yes. Since you mentioned specifically that you're using a hybrid set-up, I know with certainty that your racquet was strung in two pieces. Since the mains and crosses are tied off separately, you may be able to cut out the cross strings without losing any further tension in your mains. You'll run into some difficulty removing the knots used to start and finish the cross strings, though, depending partly on the pattern of your racquet and the kind of starting knot your stringer likes to use. Usually the starting knot uses one of the main strings as an "anchor" string—which means the starting knot is tied around the main string. This makes cutting the knot a little tricky without cutting the main string too. It can be done, but it requires a little bit of a steady hand. Depending upon whether the cross strings tie off using a main or a cross as an anchor, you may or may not have the same problem there.
But, should you remove just the cross strings and salvage try to the mains? Personally, I'd say no for a few reasons. The main reason is that over time, strings lose tension and resiliency, even if they don't break. This process actually happens over time regardless of whether the racquet is played with or not (which is why we recommend restringing at least once a year whether you've played a lot or not). So, by the time you break strings and get ready to restring, chances are that your main strings have lost significant tension and resiliency and you'd benefit from a fresh set anyway.
Additionally, cutting out just the crosses while leaving the mains means that you're exposing your racquet to a lot of uneven stress. See my post about properly cutting out strings for a little info on that topic. All in all, I think it's just a better policy to go ahead and restring the whole racquet. That way you'll know you've got a fresh, string job that's got plenty of tension and is ready to go.
So why are your cross strings breaking before your mains? Although the main strings commonly break first since they're doing most of the sliding around during ball impact, hybrid stringing changes the balance of things, so to speak. In order to compensate for mains that break more quickly, most hybrid configurations feature a more durable string in the mains (polyester is pretty popular for that, nowadays) and a softer string in the crosses. Even though the mains are still taking a beating, the use of a more durable main string may mean that it simply is going to last longer than the softer string in the crosses. The Hexy Fiber you are using in your mains is actually somewhat soft, so that may not be the cause in your case.
A second scenario is that your cross strings may have actually sustained some wear during installation. It's always important to be very careful when weaving and pulling natural gut, but some extra caution is warranted when your main strings are a geometric string with sharp edges or a textured "rough" string. There's a fair amount of friction any time cross strings are installed and geometric or textured main strings can easily damage the coating on a soft cross string, leading to premature breakage. If someone else is stringing your racquets, make sure that they take care when installing the crosses. If you're stringing your own racquets, simply pull the cross strings through more slowly and try pushing the strings down towards the throat as you do so (so it makes a big smiley) and this will help ease some of the friction. You can straighten them out once all the string is through.
Those scenarios aside, from a technique standpoint, I've also seen this happen to players who hit the ball a little later than they should. If none of the above info seems to apply, or you think you're catching the ball late, try working with a local pro who might be able to help you catch the ball further out in front of your body.
Finally, I noticed in your question you mentioned that your cross strings started showing wear pretty quickly. You didn't mention how long it normally takes for your strings to start showing wear, but I'm guessing that they usually don't wear quite that quickly. Again, it's possible that the cross strings were damaged during installation, but it's completely normal for soft strings to start "fraying" as they're played with. This is especially true if you're hitting with a fair amount of topspin.
As far as switching your string set up, I'm always encouraging people to experiment with new strings, tensions, and hybrid combinations. Even if you don't find anything you like, you can always fall back on your tried and true combination.
Hopefully I helped shed some light on your particular situation. Feel free to let us know if you have any other questions!