I overlooked your request for alternative suggestions, in my previous post.
This application would be excellent for lime-soda softening if softening was also necessary in addition to iron/manganese reduction.
Assuming that softening isn't necessary, then I recommend that you pre-oxidize the water with chlorine. Feed enough chlorine to carry a residual after the treatment process. Immediately after chlorine injection and prior to setting, add a coagulant such as filter alum to speed up the settling process. The alum dosage will probably never exceed 20 mg/L and typically will average 10 mg/L.
Pass the chemically dosed water through a settling chamber with tube settlers to accelerate the settling process. Use a loading rate of 2 gpm/sf. Lamella plates would work as well, but tubes are easier to service. Provide a hopper bottom to collect and periodically blowdown solids.
At this point, you can either gravity flow through a filter or re-pressurize using a pump and flow through a pressure filter.
The filter should be designed for a 3 gpm/sf maximum loading rate and a 15 gpm/sf minimum backwash rate for 10 minutes duration minimum. Air scour feature would be benificial for long-term operation. Simultaneous air/water wash would be desirable for reduction of backwash water volume.
The filter media can be 18" of silica sand and 12" - 18" of anthracite. The media should be coated in the field with manganese dioxide at the time of start-up. No further recoating will be necessary as long as chlorine pre-feed is maintained.
In larger volume systems, it might be desirable to consider aeration as opposed to chlorine as the primary oxidation method in order to cut down on operating cost of chemical. However, at 270 gpm the cost savings might not be that great given the added maintenance required by the heavy loading of iron and manganese and their effects on the aerator device (i.e., metal oxide build-up on slats and trays). Even using a high-efficiency aerator, you will still need to feed supplimental chlorine.
If this application is for potable water, then you should also check with your local regulatory agency in charge of water plant design for further instructions and advice.
S. Bush