Finally, there is some progress. :-)
Based on the U-Boot sources for Linksys WAG120N, I managed to create a config file for Amazon SE as follows:
0xbf800060 0x7 0xbf800010 0x0 0xbf800020 0x0 0xbf800200 0x02 0xbf800210 0x0 0xbf800230 0x0002 0xbf800220 0x30 0xbf800240 0x14c9 0xbf800280 0x36325 0xbf800290 0x81d 0xbf8002A0 0x0 0xbf800210 0x1 0xbf103010 0x20
And then used gct to convert u-boot.srec files to u-boot.asc files using the above config (amse.conf).
./gct amse.conf u-boot.srec uboot.asc
Unlike earlier attempts where I got nothing, this time after I send (paste) the u-boot.asc file into minicom, I get the UART prompt again, some sort of "reboot". This behavior is consistent, i.e., it is the same for some u-boot.asc files, while nothing happens for others. I think this is an indication that my u-boot.asc file is accepted and then rejected (sort of), which is one step ahead of not accepting at all. :-)