I don't know the Creedy, but the upper reaches of the Exe flow through bare moorland where there are essentially no trees beyond the very occasional stunted dwarf and are never going to be any. There is no "upper flood plain" - it's not like the rivers which accompany certain well-known stretches of railway in Scotland. Same goes for the Barle which is the major "upper reaches" tributary. The runoff into these rivers is moderated by the capacity of the moorland peat to absorb water, and what happens in the case of sudden peaks depends on how much rain there has been in general over the past month or two and how much of that capacity is already full. You don't get trees until you're beyond what could be described as the "upper reaches".
As for the beavers with any luck someone's dogs will find themselves a bit of entertainment.
The Cowley Bridge area has been prone to flooding ever since the railways were built, despite various measures being taken over the years on the basis of trying to get away with doing as little as possible. Surely the answer here is simply to do it properly for a change; raise it a bit more than the bare minimum and replace the embankments with low-altitude viaductlets (ie. like Langport).
Even with moorland there's plenty which can be done to encourage water storage. Especially given that whilst climate change is altering rainfall, it's not necessarily resulting in the annual total being much different (for example longer periods of dry weather in the summer being offset by more intense rainfall when we do have summer rains).
Even planning for the winter (assuming it's wetter) there's the potential of creating basins which dry out during the summer and only have standing water in more extreme periods of wet weather, with the rest of the winter they are a bit boggy.
This is all stuff which nature had been doing (including beavers, there was a town somewhere, I think Canada, which was going to do some fancy engineering only the beavers got their first and saved the council a shed load of money and basically did what the engineers said should have been done) for a very long time.
Yes there's other factors, like where we build our stuff, and sometimes we don't help ourselves (even when we're trying to fix it), however if this bridge were to become a significant single point of failure over the 20 year timeline I've mentioned, that should be a small enough project (a few tens of millions maybe) that it's not a significant cost when looking at other options.
Finally, of the 3 options (Sea wall only, DAL, via Okehampton) none of them propose a solution for this bridge and so would need to be fixed anyway.