The strategy as envisioned would
achieve few 100's microAmp average current consumption while waiting for a BLE connection
not require changing the existing BLE stack
not expose BLE radio or packet-level operating details to possible bad-guys
avoid the issue of keeping the 100kB+ size BLE code ...

My project also has the same challenge of Ultra Low Power BLE Advertising. It seems to me the challenge is twofold: (1) long time to initialize the heavy comprehensive system of ESP-IDF / Bluetooth as noted by the OP and (2) only Modem Sleep but not Deep Sleep is used. I think I see an ...

My project requires Ultra Low Power (ULP) while waiting for Infrequent Bluetooth (BLE) Connections. ESP32 was selected based on attractive Deep Sleep ULP specs, Bluetooth / WiFi capability, and overall cost & feature set. The ESP32 TRM v4.0 pg. 636 says that Deep-Sleep is "Recommended for ULP ...