Question: What is a better way of saying "in order to demonstrate this, I will..."? I already use "to that effect" in the same paragraph. I'm looking for something as compact and concise as "to that effect" that will also be a good transition for the beginning of a new paragraph.

Answer: 
I would sometimes use "to this end", however that is also more a general term. Something like: "We wish to show that space whales are secretly communicating with us. To this end, we will monitor the frequencies determined to be most likely to carry space whale song."
Is it appropriate to use "Therefore"?