Good to hear from you. (And if you don't get a follow-up answer in a day or 2 from me or anyone, e-mail 'whoever' directly. As you can see, one's posts can get pushed down awfully quick!)
Anyway, a number of things come into play here. In the next rain (when there's no lightening), and while being careful, check to see that the water in the gutters isn't backing up as a result of clogged downspouts. When you observe the top-end of the downspout where it connects to the gutter, you should NOT see the presence of water in the DOWNSPOUT. You should ALWAYS see signs of water 'begging' to go down the downspout if you know what I mean. (In other words, if you've ever had a clogged sink, you shouldn't see the same 'effect' as that.) Also, If the water COMING OFF THE ROOF (as opposed to filling up the gutter and spilling out), is the cause of the cascading, then the gutters aren't properly hung. They may be too low on the eaves, or even too high. An installation adjustment would be in order. If, on the other hand, the gutter IS FILLING WITH WATER and running out the top, then you may need to add more downspouts or correct the angle towards the downspout. And yet, if you have a 2nd story roof that drops water onto a roof below, and this roof below has a gutter for taking the water away, then there's too much water for 1 gutter system to handle. Unless the 2 roofs in question are small, then EACH roof ought to have its own gutter system. If a roof line is particularly long, sometimes each end of the gutter has a downspout. In this case, the center point of the gutter in question is the 'high' point so water runs to either the left or right downspout.
As you know, once you get the water to the gutter AND you don't have it over-flow, you then need the capacity and ability to get the water as far away from the foundation as possible, at least 3'. (We've already talked about '+' and '-' slope.) So, using your existing drainage system, go ahead and run it to the street, or to the front yard, or to a deep, filter fabric, gravel-lined well. I'd look at the too-many-roofs-going-to-one-gutter theory and the gutter-installed-too-high-or-too-low theory as to why you're having the 'cascade' problem. The angle of the gutter-to-downspout is important as far as correcting an installation problem. If there are other similiar homes in your neighborhood, go for a walk and take a look at their gutters. You'll probably note differences in height on the eaves, angle to the downspout, length of gutter, and number of downspouts. Hopefully, no one has 2 or more roof-lines going to one gutter. Again, in my opinion, each roof line should have 1 system.
Do post up here to keep us 'all' informed but do e-mail me directly saying you've done so, so I can follow-up. For now, (and until later if you need help), my best to ya and hope this helps.