In a 2016 IEEE Conference on Decision and Control paper, our team designed sequential predictors for time-varying linear systems with time-varying delays, to prove global exponential stabilization properties using a feedback control that is computed in terms of the state of the last sequential predictor. This allowed feedback delays of arbitrarily large sup norm in the original system. Here we provide a significant generalization to more challenging cases with arbitrarily large feedback delay bounds, and where, in addition, current values of the plant state are not available to use in the sequential predictors. We illustrate our work in a pendulum example.