In polar variables (x,θ) on a planar sector, we study a (1+2)D system (E2) derived from the three-dimensional axisymmetric Euler equations. Under a parity/symmetry ansatz on the whole meridian plane (odd/even reflection across the axes), we show that the velocity-pressure form of the 3D axisymmetric Euler system admits an exact reformulation in terms of Hou–Li type new variables (u,v,g). In the reformulated system (E2), the vortex stretching terms are greatly simplified (uv,v²-u²,-g²). This prompts us to treat (u,v,g) as the vorticity building blocks. Our first main result is an explicit construction of smooth solutions that blow up in finite time 0<T<∞ while a natural weighted energy remains uniformly bounded on [0,T], in particular staying finite at the blow-up time t=T. The construction proceeds in three steps. (1) We identify special ridge rays ±θ₀, 0<θ₀<π/2 such that, under the divergence-free constraint, system (E2) reduces on each ridge to a (1+1)D Constantin–Lax–Majda type convection-free reaction system in (t,x); see Theorem . (2) We then embed these (1+1)D ridge dynamics into the full sector x∈[0,∞), θ∈[-θ₀,θ₀] by introducing carefully tuned θ-dependent seed data, producing background profiles with explicit Riccati envelopes (specified via the seeds and the ridge ODE flow) that blow up only at (x,θ)=(0,±θ₀). (3) Finally, we derive the perturbation equations around this background and prove linear coercive estimates together with a conditional nonlinear control statement in high-regularity weighted Sobolev norms.