I installed esptool.py and PyFlasher GUI, and was able to install the NodeMCU variant I built at https://nodemcu-build.com Since I don't believe I have any very special needs, I went with the default modules included:
file, GPIO, net, node, timer, UART, WiFi
After flashing the BIN file to the ESP8266 successfully (with GPIO0 pulled low), I restarted the ESP and opened ESPlorer. However, ESPlorer still doesn't seem to be able to interface with the ESP. I seem to be getting very similar problems as I had earlier, when the ESP was running the "default" AT firmware.
First, I select COM7 and 115200 in the right pane, and click OPEN. This outputs:
PORT OPEN 115200
Communication with MCU...
and
Logging enable
LAFcom.sun.java.swing.plaf.windows.WindowsLookAndFeel
LAFcom.sun.java.swing.plaf.windows.WindowsClassicLookAndFeel
LAFcom.sun.java.swing.plaf.motif.MotifLookAndFeel
LAFjavax.swing.plaf.nimbus.NimbusLookAndFeel
LAFjavax.swing.plaf.metal.MetalLookAndFeel
Load saved settings: Firmware:NodeMCU
Snippets: loading...
Snippets load: Success.
Set new color theme: Success.
Load saved settings: DONE.
Snippets: loading...
Snippets load: Success.
Scan system...
found last saved serial port COM7
Scan done.
Serial port COM7 save as default.
Baud rate 115200 save as default.
Try to open port COM7, baud 115200, 8N1
Open port COM7 - Success.
sending:<CR><LF>
When I load my init.lua in the Editor (left pane) and click "Upload", I get the following output:
Try to open file init.lua
File name: C:\ESP8266 web server\init.lua
Try to load file init.lua
Loading init.lua: Success.
Open "init.lua": Success.
Uploader: Communication with MCU not yet established.