A few considerations / questions.
1. I know you have complained about the performance of your stove. How hot were your stove top temps when you were barely keeping your house 69-70?
If your stove top temps were in the 500-600 range, then I'd be concerned that your basement is solid concrete and it is soaking up all of the heat and sending it out to the earth through your uninsulated basement walls rather than keeping it in your home.
2. I know you said this was dead standing wood that was cut and split 7-8 months. However, from what I see in the corner that does not look seasoned to me. Have you tried out a moisture meter yet? Additionally, if you are loading the stove w/ nothing but rounds, you won't get poo for a fire going. Rounds are great for loading in between splits, but in general, you need a mix. Also, rounds take longer to season than splits since evaporation can only take place through the ends.
3. Regardless, w/ the size of your flue I'd say a liner is a good idea. But if that wood is not perfect, you will not get the results you ever want. Especially when you factor in that you are heating from an uninsulated concrete basement.
4. How much wood are you putting on this fire? If I start a small fire in a cold stove I don't get a lot of heat from this thing. My heat comes from first having a fire to get some coals going, then loading the old girl up w/ wood (filling it right up to the top of the fire bricks), then letting her do her magic. Also, if all you have are these rounds, go to the grocery and buy a cart full of their wood splits and give it a go.
Good luck.
pen