Can I work in the gap between my OPT ending / SEVIS transfer and my CPT starting?

No - and this rule protects you. The day your SEVIS transfers out, your OPT ends; from then until your CPT takes effect, you can't work. The standard move: unpaid leave for that window. We shrink the gap by timing the transfer well and, if needed, using a school that allows CPT up to 30 days before the term.