***** NOT A TEACHER *****
In my humble opinion, you are spot-on.
You decided to change two sentences into a compound sentence:
"Television has many programs, and [it] thus gives viewers a wide choice."
Furthermore, as you correctly implied, the -ing version is often introduced by "thus":
"Television has many programs, thus giving viewers a wide choice."
In fact, if I understand my books correctly, all of these different versions are just a variation of:
"Television has many programs, so that it gives viewers a wide choice."
James
If I have imparted any accurate information, all credit goes to George Oliver Curme in his A Grammar of the English Language, published in 1931 but containing historical material, most of which has NOT been discredited up to 2014.