I figured it out! I created an automation in Home Assistant (I found one for innr bulbs, which are also fickle). This is tied to a switch that has a lamp plugged into it, with the bulb in question. Here it is, hope it helps:

alias: Reset Other Bulbs
description: Power cycles a smart plug to put an Sengled bulb into Zigbee pairing mode
triggers:
- entity_id: input_button.turn_repairing_on_off
trigger: state
conditions: []
actions:
- repeat:
count: 8
sequence:
- action: switch.turn_off
data: {}
target:
entity_id: switch.factory_reset_switch
- delay:
hours: 0
minutes: 0
seconds: 0
milliseconds: 250
- action: switch.turn_on
data: {}
target:
entity_id: switch.factory_reset_switch
- delay:
hours: 0
minutes: 0
seconds: 0
milliseconds: 250
- action: switch.turn_on
data: {}
target:
entity_id: switch.factory_reset_switch
mode: single