Really delete old checkpoints this time.

Follows up on cl/188187349, which fixed checkpoint management for tf.train.Saver
when executing eagerly. Except I was recreating the tf.train.Saver objects each
save, so tfe.Checkpoint and friends did not benefit from that change.

Keeps the same tf.train.Saver around when executing eagerly. This limits object
graph mutations just like when graph building; if there are complaints I can
assign to Saver._var_list instead, since eager tf.train.Saver is not specialized
to its var_list argument.

PiperOrigin-RevId: 189211552