"The pumping operation is currently centred on the areas of Curry Moor, Moorland and Langport. "
http://www.bbc.co.uk/news/uk-england-somerset-20575152
For what it's worth, Google Earth shows that the canal upstream from Bridgewater is about 20m (~65ft) wide at the banks, maybe half that in the stretches photographed at low(er) tide. Well beyond the reach of a JCB, so the most they could manage would be to peck at the riverbank (which explains the environmentalist concerns viz otter/water vole et al) and just hope that the river redistributes silt from the centre out to the edges again by the following year.
If draft is a major issue then a canal barge conversion is the logical step. How did they manage the upkeep, historically, I wonder?
Trouble is, though, since the Dutch did their handiwork, half a dozen bridges have gone up on the stretch to Langport, Muchelney etc.
I can't help thinking that a better fix would be to cut a complete new river-sized canal but Labour-cost-wise, it's 150 years too late to bring in navvies.