The uncertainty on the laminar flame speed extracted from spherically expanding flames can be minimized by using large flame radius data for the extrapolation to zero stretch-rate. However, at large radii, the hydrodynamic and thermo-diffusive instabilities would induce the wrinkling of the flame surface and limit the range of usable data. In the present study, we have employed the flame stability theory of Matalon to tailor the properties of the initial mixture so that onset of cellular flame would occur at a pre-determined, large radius. This approach was employed to measure the laminar flame speeds of H/O/N/He mixtures with equivalence ratios from 0.6 to 2.0, at pressures of 50/80/100 kPa and initial temperature of 300 K. For most experiments we performed, the uncertainty related to the extrapolation to zero stretch-rate (performed with the linear curvature model) was below 2% as shown by the position of the data points in the (L/R, L/R) plan, where L is the burned Markstein length; and R and R are the flame radii at the lower and upper bounds of the extrapolation range. Unsteady 1-D simulations using four chemical mechanisms were performed to show that unstretched laminar flame speed can be well-characterized with relative error below 10% for most conditions. The flame dynamical response to stretch rate could be captured by the mechanisms only under some conditions. Further analyses on critical flame radius were carried out: (i) the dominant parameters were identified based on a local sensitivity analysis; and (ii) the uncertainty on the predicted critical radius was determined through an uncertainty propagation approach. Uncertainty in critical flame radius calculation comes mostly from the uncertainty on fundamental transport and kinetic data. The present work indicates that although the stability theory of Matalon provides a well defined framework to tailor the mixture properties for improved flame speed measurement, the inaccuracy of some of the required parameters can result in significantly over-estimated critical radius for cellular flame onset which compromises the accuracy of the tailoring procedure.