Some of the distinctions being tossed about such as farmed vs. managed lumber are just matters of semantics and essentially mean the same thing. And lumber today is NOT the same as yesterday's lumber and the difference is less related to sapwood vs. heartwood than it is the age and size of the trees when harvested and the resulting radius of the growth rings. How the wood is milled is also a factor. A piece of wood shrinks and swells at different rates along its various planes. Movement is greatest along the circumference of its rings. That is why a cut cross section of trunk, or "tree cookie" often used for craft projects, splits in one or more places as it dries. On old growth wood, not only are the rings closer together, which makes for stronger wood, but the the larger trees have a larger or "flatter" radius, resulting in less warping as it seasons. This is why antique table tops are often seen made from wider boards than those made today, which must be edge-joined out of narrower boards to minimize warping. If you look at the ends of a board and you see a distinct curve to the rings, you have wood that will likely curve or warp with humidity changes.
While wood from trees harvested at a smaller size to meet today's demand have more issues than old growth timber, the method used to mill the logs can make a huge difference. Construction grade lumber is normally milled by a method called plainsawing, which results in the less waste, but the poorest performing lumber. But for structural framing, it is "good enough". If you must use 2x4s, I'd suggest you dig through the pile looking for boards that were quartersawn or riftsawn. Doing a web search on those terms will give better visuals than I can describe. The best solution has been given multiple times in previous posts. L-girder construction using standard pine boards will be much more stable and more than strong enough. Poplar is nice but not necessary. Just don't use the cheapest grade of pine. Knotty pine is great for paneling but not for framing!
