Before revision:  A diverse array of numerical illustrations are presented, along with the MATLAB code for reproducing the results in a publicly available at repository URL A number of open problems are discussed, and an appendix containing all algorithms type-set in a uniform fashion is provided.
After revision:  Additionally, new block versions of low-synchronization variants are derived, and their efficacy and stability are demonstrated for a wide range of challenging examples. Low-synchronization variants appear remarkably stable for s-step-like matrices built with Newton polynomials, pointing towards a new stable and efficient backbone for Krylov subspace methods. Numerical examples are computed with a versatile MATLAB package hosted at URL and scripts for reproducing all results in the paper are provided. Block Gram-Schmidt implementations in popular software packages are discussed, along with a number of open problems are discussed, and an appendix containing all algorithms type-set in a uniform fashion is provided.