No, not a good idea, it's even a bad idea. A lower temp thermostat won't prevent overheating but will drastically lower MPG and could really effect other temp sensitive, computer controlled, and emissions items.
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To prevent overheating you need to increase the efficiency of your cooling system, several things can be done. By far the easiest is tweaking the coolant, if you are running 50/50 anti-freeze, don't. Water is a much better coolant then the anti-freeze additive. You only need enough additive in your coolant for two things, to prevent corrosion, and to prevent freezing in the temps you actually experience. It's very unlikely you'll experience -30F in California, so why give up cooling efficiency for that level of protection. Next would be some form of SCA(super coolant additive), we IDI and other diesel owners should be very familiar with SCAs in one form or another, there are many forms/products, I'm not the be all end all off experts on the subject yet. But for you some of the products like the Water Wetter from Redline and others easily and cheaply offer both an increase in coolant efficiency and some anti corrosion properties. They help the cooling system by helping with the transfer of heat between the metal and water, they do this IIRC in part by creating a heat transfer coating and in part by breaking down the surface tension of water so it makes better contact with the metal. An interesting note is that some used soap for this back in the day.
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(addition) It's been a while but the last gas powered vehicle I had that had overheating issues I ran a combination of distilled water, 20% anti-freeze, and a bottle of water wetter. Made a real difference, and I only ran so much anti-freeze cause I'm in the Seattle area, likely less would be needed if you stay in SoCal.
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Personally I'd hook the transmission cooler back to the radiator, constant ATF temps are as important as temps that aren't too hot. So maybe have it run from tranny, to aftermarket cooler, to radiator cooler, to tranny.
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Not an expert on your rig, does it have an engine oil cooler? Some have a radiator cooler, and many GMs have an oil water heat exchanger mounted with the oil filter, if you don't I'd consider it, cool gizmo.
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Next would be a bigger radiator, then more air flow, etc.
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Edit, one more, increasing the timing on your engine may help a lot. An engine with more timing to a point not only runs cooler but get's more MPG and makes more power. But cause it's to a point where going too far can cause damage the stock settings are generally very conservative. On most engines, in particular domestic V8s, a bump of 2-6 degrees can really make a difference.
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OK one more edit, that the increase in coolant temps coincides with an increase in RPM may be a sign of a water pump issue. At high RPM the coolant in the water pump may be cavitating, several things can cause this and several options are available. Does it ever over heat going slow, or does it lose coolant?
The colder stat will throw a code. Using the reading from the IAT , the PCM calculates the time needed to reach operating temperature. If this time is too slow , it sets a code. This is to detect a stuck thermostat. That said, it can be fooled 