The trisaccharide 1-kestose, a major constituent of commercial fructooligosaccharide (FOS) formulations, shows a superior prebiotic effect compared to higher-chain FOS. The plant sucrose:sucrose 1-fructosyltransferases (1-SST) are extensively used for selective synthesis of lower chain FOS. In this study, enhanced recombinant (r) 1-SST production was achieved in Komagataella phaffii (formerly Pichia pastoris) containing three copies of a codon-optimized Festuca arundinacea 1-SST gene. R1-SST production reached 47 U/mL at the shake-flask level after a 96-h methanol induction phase. A chemostat-based strain characterization methodology was adopted to assess the influence of specific growth rate (µ) on cell-specific r1-SST productivity (Qp) and cell-specific oxygen uptake rate (Qo) under two different feeding strategies across dilution rates from 0.02 to 0.05 h. The methanol-sorbitol co-feeding strategy significantly reduced Qo by 46 ± 2.4% compared to methanol-only feeding without compromising r1-SST productivity. Based on the data, a dilution rate of 0.025 h was applied for continuous cultivation of recombinant cells to achieve a sustained r1-SST productivity of 5000 ± 64.4 U/L/h for 15 days.