Before changing anything, back up the FIP partition if there is any chance you will want the factory firmware again. Keep that backup safe for the restore step, and a prepared FIP backup can also be used later if needed.
The FIP partition is read-only by default. To unlock firmware flashing, first write cudy_tr3000-v1-sysupgrade.bin. In the router's admin panel, go to Basic Settings -> Firmware Upgrade, choose that file, and start the write.
After the reboot, you will land on the upgrade page for the transitional OpenWrt firmware. Flash openwrt-mediatek-filogic-cudy_tr3000-v1-squashfs-sysupgrade.bin.
When it comes back up, log in at 192.168.1.1 with password password. OpenWrt is now installed.
Adding U-Boot
Flashing U-Boot now makes future experiments easier. Two U-Boot files are available: one for the original partition layout and one for a larger partition layout. Pick according to your plan.
In OpenWrt, go to System -> File Transfer and upload the U-Boot file you need to /tmp/upload.
Then open System -> TTYD Terminal. Log in as root with password password, and run the matching command set.
For the original partition layout, flash mt7981_cudy_tr3000-v1-u-boot.fip (access password: 3705):
cd /tmp/upload/
mtd write mt7981_cudy_tr3000-v1-u-boot.fip FIP
For the larger partition layout, flash mt7981_cudy_tr3000-mod-u-boot.fip (access password: 3705):
cd /tmp/upload/
mtd write mt7981_cudy_tr3000-mod-u-boot.fip FIP
Reboot afterward. To use U-Boot for future flashing, connect an Ethernet cable to a LAN port, set a static IP of 192.168.1.10, and hold Reset for about 10 seconds. When the indicator changes from blinking to solid red, open http://192.168.1.1/.
One note: if you switched to the larger partition layout, use firmware images whose names do not include v1.
Returning to the factory firmware
Connect via a LAN port and set the computer to static IP 192.168.1.10. Hold Reset and open http://192.168.1.1/uboot.html.
Choose your own FIP.bin backup, or a prepared FIP backup, then upload and flash it. The router will restart on its own.
Next, set the computer to static IP 192.168.1.88 with gateway 192.168.1.112.
Run a TFTP server and upload recovery.bin. Unplug power, hold Reset, and power the router back on to start recovery.