Hi Tyan.
"Browning out" the spatterdock's lily pads isn't a huge challenge.
Controlling spatterdock roots (tubers) is a different story.

I've had relatively few encounters with spatterdock; so my comments are mostly speculation in respect to this species.
I suspect that glyphosate-based products will offer reasonably decent brown-out of exposed/treated spatterdock pads; but may not provide satisfactory control of the tubors that are buried in the hydro soil.
For topical pad-treatments, I think an imazapyr-type herbicide would offer better odds of yielding greater impact on spatterdock roots. Either way, repetitive treatments will likely be necessary as new pads reach the surface (which were not contacted by a previous treatment).
Use a quality methylated seed-oil (MSO) surfactant for better adhesion to and penetration of treated pad-surfaces. This is critical, since the pads of all lily-species tend to shed spray-droplets quite readily - unless the proper adjuvant is utilized.
Personally, I would attack this type of weed infestation more aggressively that I would a fully submerged species (such as coontail), or algae infestations. In other works, I probably wouldn't follow the old rule-of-thumb to treat only 1/3 of the pond at a time. Spatterdock is a comparatively fibrous plant that decomposes more slowly than algae or fleshy submerged plants. I�ve never heard of a fish-kill related to DO crashes behind a lily treatment; although I suppose it is possible. From a DO standpoint, I�m more concerned about aggressive algae treatments, since this simple organism dies and decomposes quite rapidly - and the �bugs� (microbes) that digest (decompose) the dead algae use vast amounts of oxygen during the process � and are also much more prone to accelerated population-spikes due to the shear amount of readily available nutrients.
Although dead lily species also decompose through microbial means, they�re relative biomass is nowhere near that of a submerged weed-infestation (coontail, Hydrilla, milfoil, etc). Therefore, in most scenarios I�ve encountered, dead lilies don�t appear to support the level of microbial activity that threaten a DO-crash. If someone has experienced otherwise, I�m all ears�.