Decoherence of quantum systems due to uncontrolled fluctuations of the environment presents fundamental obstacles in quantum science. Clock transitions which are insensitive to such fluctuations are used to improve coherence, however, they are not present in all systems or for arbitrary system parameters. Here we create a trio of synthetic clock transitions using continuous dynamical decoupling in a spin-1 Bose-Einstein condensate in which we observe a reduction of sensitivity to magnetic-field noise of up to four orders of magnitude; this work complements the parallel work by Anderson et al. [R. P. Anderson et al., following paper, Phys. Rev. A 97, 013408 (2018), 10.1103/PhysRevA.97.013408]. In addition, using a concatenated scheme, we demonstrate suppression of sensitivity to fluctuations in our control fields. These field-insensitive states represent an ideal foundation for the next generation of cold-atom experiments focused on fragile many-body phases relevant to quantum magnetism, artificial gauge fields, and topological matter.