It would appear that DM1106EN behaves slightly differently from the DTM0660L when it comes to EEPROM location/settings:
- EEPROM location 0xFC (backlight timeout) seems to be in minutes (vs on DTM0660L its in seconds).
- EEPROM location 0xFA Bit 1 (enable Serial UART output via long press of "REL") doesn't seem to enable UART
I sniffed the I2C bus for the EEPROM activity to get better understanding what EEPROM locations meter appears to be using (reading).
Following shows the changes (highlighted in red) that I've made to factory settings (so you'll see the data from "90dm600-hack.bin" being read by the meter on the captures):

Meter power up (to "V~" mode):
54556-55231 24xx EEPROM: Operations: Sequential random read (addr=F8, 6 bytes): 5A C6 EC 1E 0A 00
55250-56527 24xx EEPROM: Operations: Sequential random read (addr=10, 15 bytes): 10 27 0F 27 DE 03 66 66 3D 3D FF 3B 0A FF 40
56546-57621 24xx EEPROM: Operations: Sequential random read (addr=33, 12 bytes): 04 12 09 6B F8 0A D0 1B 0A 1A 01 0A
57642-58250 24xx EEPROM: Operations: Sequential random read (addr=0B, 5 bytes): 0E 01 E8 D4 03
58269-58812 24xx EEPROM: Operations: Sequential random read (addr=20, 4 bytes): BB 99 1B 81
58831-60041 24xx EEPROM: Operations: Sequential random read (addr=40, 14 bytes): 00 01 00 01 00 07 98 00 64 00 64 00 64 00
60060-60468 24xx EEPROM: Operations: Sequential random read (addr=4E, 2 bytes): C0 00
60492-61167 24xx EEPROM: Operations: Sequential random read (addr=2A, 6 bytes): 2D 8D AD 8D 95 F7
357725-358066 24xx EEPROM: Operations: Random access read (addr=8E, 1 byte): 04
358086-358427 24xx EEPROM: Operations: Random access read (addr=9E, 1 byte): 00
358447-358788 24xx EEPROM: Operations: Random access read (addr=AE, 1 byte): 00
358808-359148 24xx EEPROM: Operations: Random access read (addr=BE, 1 byte): 00
359208-360417 24xx EEPROM: Operations: Sequential random read (addr=40, 14 bytes): 00 01 00 01 00 07 98 00 64 00 64 00 64 00
360436-360844 24xx EEPROM: Operations: Sequential random read (addr=4E, 2 bytes): C0 00
360866-361275 24xx EEPROM: Operations: Sequential random read (addr=28, 2 bytes): 00 80
361305-361720 24xx EEPROM: Operations: Sequential random read (addr=E6, 2 bytes): DB 7F
Switching to range "V~":
11-353 24xx EEPROM: Operations: Random access read (addr=8E, 1 byte): 04
373-714 24xx EEPROM: Operations: Random access read (addr=9E, 1 byte): 00
734-1075 24xx EEPROM: Operations: Random access read (addr=AE, 1 byte): 00
1094-1435 24xx EEPROM: Operations: Random access read (addr=BE, 1 byte): 00
1494-2704 24xx EEPROM: Operations: Sequential random read (addr=40, 14 bytes): 00 01 00 01 00 07 98 00 64 00 64 00 64 00
2723-3131 24xx EEPROM: Operations: Sequential random read (addr=4E, 2 bytes): C0 00
3153-3561 24xx EEPROM: Operations: Sequential random read (addr=28, 2 bytes): 00 80
3592-4007 24xx EEPROM: Operations: Sequential random read (addr=E6, 2 bytes): DB 7F
Switching to range "V":
12-353 24xx EEPROM: Operations: Random access read (addr=8F, 1 byte): 03
373-713 24xx EEPROM: Operations: Random access read (addr=9F, 1 byte): 00
733-1074 24xx EEPROM: Operations: Random access read (addr=AF, 1 byte): 00
1094-1434 24xx EEPROM: Operations: Random access read (addr=BF, 1 byte): 00
1492-2702 24xx EEPROM: Operations: Sequential random read (addr=40, 14 bytes): 00 01 00 01 00 07 98 00 64 00 64 00 64 00
2721-3129 24xx EEPROM: Operations: Sequential random read (addr=4E, 2 bytes): C0 00
3152-3827 24xx EEPROM: Operations: Sequential random read (addr=2A, 6 bytes): 2D 8D AD 8D 95 F7
8483-8891 24xx EEPROM: Operations: Sequential random read (addr=E6, 2 bytes): DB 7F
Switching to range "mV":
11-353 24xx EEPROM: Operations: Random access read (addr=8C, 1 byte): 01
373-714 24xx EEPROM: Operations: Random access read (addr=9C, 1 byte): 02
734-1075 24xx EEPROM: Operations: Random access read (addr=AC, 1 byte): 00
1095-1436 24xx EEPROM: Operations: Random access read (addr=BC, 1 byte): 00
1493-2703 24xx EEPROM: Operations: Sequential random read (addr=40, 14 bytes): 00 01 00 01 00 07 98 00 64 00 64 00 64 00
2722-3130 24xx EEPROM: Operations: Sequential random read (addr=4E, 2 bytes): C0 00
3153-3829 24xx EEPROM: Operations: Sequential random read (addr=2A, 6 bytes): 2D 8D AD 8D 95 F7
Switching to "Ohm":
12-353 24xx EEPROM: Operations: Random access read (addr=8D, 1 byte): 07
373-714 24xx EEPROM: Operations: Random access read (addr=9D, 1 byte): 0A
734-1075 24xx EEPROM: Operations: Random access read (addr=AD, 1 byte): 09
1094-1435 24xx EEPROM: Operations: Random access read (addr=BD, 1 byte): 0B
1482-2291 24xx EEPROM: Operations: Sequential random read (addr=60, 8 bytes): C4 7F BD 84 01 00 0C 2B
2311-3387 24xx EEPROM: Operations: Sequential random read (addr=70, 12 bytes): 28 80 00 80 A4 83 E8 7D 0A 27 00 00
Switching to mode "Hz":
12-353 24xx EEPROM: Operations: Random access read (addr=8B, 1 byte): 12
373-714 24xx EEPROM: Operations: Random access read (addr=9B, 1 byte): 13
734-1075 24xx EEPROM: Operations: Random access read (addr=AB, 1 byte): 15
1095-1436 24xx EEPROM: Operations: Random access read (addr=BB, 1 byte): 00
Switching to mode "10A":
12-353 24xx EEPROM: Operations: Random access read (addr=86, 1 byte): 10
373-714 24xx EEPROM: Operations: Random access read (addr=96, 1 byte): 11
734-1076 24xx EEPROM: Operations: Random access read (addr=A6, 1 byte): 00
1095-1443 24xx EEPROM: Operations: Random access read (addr=B6, 1 byte): 00
1500-2710 24xx EEPROM: Operations: Sequential random read (addr=40, 14 bytes): 00 01 00 01 00 07 98 00 64 00 64 00 64 00
2728-3136 24xx EEPROM: Operations: Sequential random read (addr=4E, 2 bytes): C0 00
3160-3835 24xx EEPROM: Operations: Sequential random read (addr=2A, 6 bytes): 2D 8D AD 8D 95 F7
Switching to mode "mA":
12-353 24xx EEPROM: Operations: Random access read (addr=87, 1 byte): 0E
373-714 24xx EEPROM: Operations: Random access read (addr=97, 1 byte): 0F
734-1075 24xx EEPROM: Operations: Random access read (addr=A7, 1 byte): 00
1094-1435 24xx EEPROM: Operations: Random access read (addr=B7, 1 byte): 00
1492-2702 24xx EEPROM: Operations: Sequential random read (addr=40, 14 bytes): 00 01 00 01 00 07 98 00 64 00 64 00 64 00
2721-3129 24xx EEPROM: Operations: Sequential random read (addr=4E, 2 bytes): C0 00
3152-3827 24xx EEPROM: Operations: Sequential random read (addr=2A, 6 bytes): 2D 8D AD 8D 95 F7
Switching to mode "uA":
12-354 24xx EEPROM: Operations: Random access read (addr=8A, 1 byte): 0C
374-715 24xx EEPROM: Operations: Random access read (addr=9A, 1 byte): 0D
735-1076 24xx EEPROM: Operations: Random access read (addr=AA, 1 byte): 00
1096-1443 24xx EEPROM: Operations: Random access read (addr=BA, 1 byte): 00
1500-2710 24xx EEPROM: Operations: Sequential random read (addr=40, 14 bytes): 00 01 00 01 00 07 98 00 64 00 64 00 64 00
2729-3137 24xx EEPROM: Operations: Sequential random read (addr=4E, 2 bytes): C0 00
3160-3835 24xx EEPROM: Operations: Sequential random read (addr=2A, 6 bytes): 2D 8D AD 8D 95 F7