Equal balance on all covariates is neither a goal of randomization, nor a requirement for proper statistical assessment of a randomized experiment. Any statistic you calculate that assumes randomized assigned took place already accounts for any imbalances on both known and unknown covariates, even if there are infinitely many of these. Re-randomization is therefore unnecessary at best. Stephen Senn's work on this is very good.

Blocking is nice-to-have when possible and cost-efficient, but from what I know it is typically neither. If one does blocking, then the corresponding statistic should reflect that, otherwise it will report an inflated uncertainty.