Can an infinitely generated Fuchsian group change its critical exponent without leaving one quasiconformal deformation space? This anonymous, unrefereed candidate gives an all-Fuchsian construction. Start with a closed surface of genus at least two and map its fundamental group onto a nonabelian free group by killing a complete cut system. The fixed kernel defines a regular normal cover. For every marked compact hyperbolic metric, its Fuchsian image is infinitely generated and of the first kind. Because the deck group is nonamenable, a theorem of Dougall and Sharp forces the critical exponent below one. Now pinch every cut curve to the same small length. A function supported on one lifted cell changes only across fixed-width pieces of the long collars, so its spectral energy is proportional to the pinching length while its mass stays bounded below. Sullivan's spectrum-exponent formula then makes the critical exponent approach one from below, at a linear one-sided rate. Therefore it takes infinitely many distinct values. The scope is important. Astala and Zinsmeister appear already to provide an affirmative precedent under a broad quasi-Fuchsian reading of the AIM problem. This candidate stays entirely in the Fuchsian locus and is a direct AIM solution candidate only under the reduced surface-based reading. Producer replay and internal editorial checks are not independent reconstruction, external specialist review, formal verification, peer review, novelty or priority evidence. The synthetic-voice briefing is a communication aid, not additional mathematical evidence.