My guess is that he tried it without the table first and was unsuccessful so he got the table. There was also a shirt tied around her neck and that may have hampered his ability because it was somehow entwined where he could cut. That shirt could also explain why his DNA wasn't on the rope.
JMO
If he touched the shirt (and he had to if he removed it from her mouth) shouldn't his DNA be on the shirt? We were told I believe, that no one's DNA was found except RN's.