Personally, I would ignore all that mumbo-jumbo from the dictionaries. There are only two basic principles to remember (in bold font below).
1. If it means "therefore" (i.e., "because of this", "as a consequence of what was just said"), use so, not so that. This form introduces an independent clause, so you use a comma. The main clause tells why the action in the so clause occurred.
My throat was sore, so I went to the doctor. [I went to the doctor? Why? Because my throat was sore.]
She wanted a car, so I gave her some money.
Her socks were worn out, so she threw them in the trash.
There are no buses, so you have to walk.
Larry's TV can't be repaired, so he's going to buy a new one.
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2. For other meanings, you can use either so or so that. [in such a way (that), in such a manner (that), with this motive: that ..., for this purpose: that ..., in order that] In this pattern the main clause does not tell why the action in the so (that) clause occurred. In fact, it's often the reverse. The so (that) clause expresses an action that is desired, not an action that necessarily occurred.
He lowered his voice so (that) Dora couldn't hear. [He lowered his voice. Why? Because he didn't want Dora to hear.]
Jane hung the picture so (that) everyone could see it.
Louise portioned out the cake so (that) there would be two pieces for each person.
I'll give you a map so (that) you won't get lost.
She worked hard so (that) everything would be ready in time.
Start early so (that) you won't have to hurry.
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Further notes:
The relationship can sometimes be seen either way. You can only include that if you're not thinking "therefore", but some other relationship.
The gravestones were covered with moss, so (=therefore) it was impossible to read the names on them.
The gravestones were covered with moss so (that) (=in such a way that) it was impossible to read the names on them.
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I find the following somewhat unusual.
Nothing more was heard from him so that we began to wonder if he was dead.
I think the author's intent here is Nothing was heard from him for such a long time that we began ....
But I would have written:
Nothing more was heard from him, so we began to wonder if he was dead.
because I feel the sense of "therefore" more strongly in that sentence.
Sometimes it's a matter a translating your personal thoughts as you feel them! 
CJ