I don't think that a deep cycle battery would be worth any cost premium, as our original flooded batteries were very well managed and used very little water. My original starting battery still tested quite good after 6 years when it was replaced to eliminate that variable at the urging of others, and then I used it to crank my lawn tractor for one more season before letting the next winter finally kill it..
Here's a summary from our OBC failure survey...
1. Year and mileage on your iMiev: 2012 - 91,000
2. OBC failure experience: Filter caps and 20A fuse blew at 80,000 miles, 6 yrs old
3. 12V Battery Condition, Age: Healthy V and CCA at 6 yrs, replaced along with OBC, still in use on another vehicle.
4. 12V Battery Maintenance Frequency and Procedures: Watered at least once per year, consumption was low.
5. No timer use, but unplugged during L1 charging a few times.
My 12V lived a hard life with extended accessory use and many ICE jump starts, but OBC/DCDC failed overnight on a normal L2 recharge in mild weather.
2012 i-SE "MR BEAN" 110,300 miles
2016 KIA SOUL EV, 90 kW, 27 kWh, 34k miles
2000 Mazda Miata EV, 78 kW, 17 kWh
1983 Grumman Kurbwatt EV,170 kW, 32 kWh
1983 Mazda RX-7 EV 43 kW 10 kWh
1971 "Karmann Eclectric" EV 240 kW 19 kWh