Check your math!
A typical battery is 100 amp hours.
So- lets say -worst case- one draws 200 amps for 30 seconds or seen another way 1/120 of an hour.
That isn't gonna take the battery down to "20%-40% of it's capacity" In fact a good battery, ie not worn out or defective, should do this many times before reaching even 40% of capacity.
And your statement- "For the record, Marine batteries are a "hybrid" of starting and deep-cycle batteries."
You can fix that for you by adding the word some after the first comma.
"Marine" batteries are available in 3 types- deep cycle, starting, and dual purpose starting/deep cycle.
I agree with Diamondpilot the "marine dual purpose" batteries are probably the best way to go. Especially if one is dumping a lot without recharge between cycles. Some deep cycle batteries just simply aren't designed to put out the massive current needed for a dump trailer. As I said one source says to use a 20% greater size battery if using a true deep cycle battery as a "starting" or dump trailer lifting battery.
Now personally I haven't used my dump trailer to dump frequently without recharge, I always have a road trip to get more material to bring it back up before the next cycle.