Your saying that doesn't make all phenolic tubing the same. At least you are giving us a hint of the problem. I'll bet if you say what brand and size of phenolic tubing, someone with knowledge about that in particular will jump in with more grounded advice.
Phenolic laminates can be obtained that are reinforced with paper, linen, canvas or fiberglass. And I'd guess a few other things as well. Something tells me that a thick, glass reinforce phenolic laminate in a light rocket will have far less trouble than a thin, paper reinforce phenolic laminate in a heavy rocket. But you are leaving any engineers (as opposed to invokers of magic amulets and true names) in the dark. Just saying "phenolic tubing" is like just saying "epoxy tubing" and pretending that epoxy/glass is the same as epoxy/carbon, epoxy/Kevlar, epoxy/S2 glass, epoxy/basalt, epoxy/paper (something I've messed around with), epoxy/whatever.
Incidentally, if you care about weight, the lightest thing might be to create crack stoppers* with thin rings at intervals on the inside of the tubes. Well, that's for lengthwise cracks. If they're going the other way, use long, thin stringers. You COULD put them on the outside, but it would look funny, and be a bit draggier. Maybe not a lot draggier if the reinforcement was thin and the boundary layer was thick at that point.
The rings or stringers wouldn't actually have to be fiberglass. Thin wood veneer would work fine, too. And many other materials. I once had a model airplane fuselage which I'd finished with water-based urethane instead of plastic covering. Turns out that the plastic had a function and it cracked easily. It looked funny, but a few rings of thread on the outside stopped the problem.
*Much like rip stop in fabric.
