How can I signal a USB charger to provide power?
Power delivery from power packs doesn't need enumeration. As a matter of fact, none of standard power schemes do this, the entire power delivery or older battery charging protocols/handshakes don't rely on USB enumeration. Battery charging was intentionally specified outside the USB in-band signaling protocol. 

However, many powerbanks have a design feature to shut itself down if the current drawn from it falls below 50-70mA.

Try to add an extra load (like 47 Ohms resistor), or find a powerbank that doesn't have the cutoff threshold. For more details see this discussion. There are references to models that don't have the shut-off.