Regarding stripping down your trainer for parts.. well, as I've said before, most people keep their trainers. If you do strip it down, I can pretty much guarantee that you will be back to looking at putting it back together and flying it.. sooner than you think. It's always nice to go back to basics and just fly the simple trainer. It sort of humbles you a tad because you will find that you will get more capable aircraft and proficient with those.. then going back to the basics, you will proibably have to 'relearn' some of the basic stuff which will really improve your flying the more advanced stuff.
As far as the CUB is concerned.. I would not get it as a second plane, I would opt for a more capable 'trainer' type as a Tiger II or 60, Four Star 40 or 60, or even a Goldberg Protege or something on that order. All very capable yet doscile enough so that you can smoothly progress through that stage. Then perhaps the CUB would be a good one.
Believe me, if I could do anything I wanted, I would keep the Nexstar flight worthy (and probably buy 2 planes right now, a cheap basher and the cherokee, to fly in that order). If I get something super cheap then maybe I will get more electronics and a new engine. The way I see it is I can only fit one plane in my car to bring to the field. If I crash, I can switch out radio gear and engine the night I get home and reload the trainer. Especially if my second plane is just yet another tool/stepping stone to get to where I want to be, I don't see why I should sink any more money than absolutely necessary into it, which is why I will go for a cheaper imitation rather than a 4 star or Tiger II.
I don't know where the CUB was mentioned - is this another name for Cherokee?
As far as the way a plane flies, the only concerns I really have are severe stalls. It will be a while before I have #2 airborne, and I will be taking off and landing, over and over again, slow speed, high speed, steep approaches and gradual approaches, until I am a champion at take off and landing. If I know my second plane lands hot, then I will land my Nexstar hot and get it right and be confident before I take the second plane out. And I will use the buddy box on my second plane. I have used the simulator with sport planes, and while it's not the same as real flying, I believe it has made me a very good flier for a beginner. I can perform any move that has been asked of me, and am constantly complemented and congratulated at the field for the progression I've made. I feel that I will be ready for a more responsive plane as soon as I stick my landings a little better.
I got into this hobby because I love the look of a scale looking RC plane, both whizzing by in the air and on a shelf. It's mildly disheartening to think that I need to go through at least two planes, and just under $1000, before I can fly one. I don't feel like I am asking a lot with that. However I understand and appreciate and respect what you all are telling me. I get a lot of enjoyment out of flying a pretty looking plane, again, why I got the Nexstar (one of the best looking trainers IMO). It looks pretty cool at a low altitude pass, but terribly unrealistic at a high speed, low(ish) altitude pass with a 80 degree, tight banking turn. A guy at my field has a Cherokee, and it just looks a lot better at sport flying maneuvers.
There is the Pacific Aeromodels Knockabout Cherokee, which to me, is the best looking plane I've seen yet! Probably my favorite as far as looks go. But for the same price (with Tower discounts and rebate form) I can get the Great Planes Cherokee, with flaps, 7 servos, a huge removable canopy (though not as nice looking IMO) so that seemed to make more sense, as it would be like a second -> third plane transition.
So, at this point, the options are:
Great Planes Cherokee ARF - Good looking plane, has flaps

, probably needs flaps to land because it's heavy with a heavy wing loading[&o].
Pacific Aeromodels Knockabout Cherokee - best looking, fair value, more of a standard second plane? Similar to the above with a lighter wing loading ('cause only 4 servos?) Also this plane is set up so that it can easily be made a tail dragger

Great Planes Super Sportster - really good looking, have to get used to hot landings,
Nitromodels Super Low Wing Trainer - fair looking and cheap, won't be afraid to go nuts with it, though might be disappointed I don't have one of the two above.