So here's the good news. It's not a fungus.

Instead, it shows the plant ran short of water last year. Likely during a hot spell. Probably not fully rooted in as yet. Usually takes at least two years of regular irrigation.

Wow. are you sure? Having some leaves with brown radiating out from the center vein doesn't seem like a lack of water symptom?

What could I do to verify it isn't a fungus?

Maybe take some leaves into the local Co-op?

I agree that is not a disease, it's a moisture issue. And of course then there are the weevils...

Do you feel you have reduced those numbers, are you finding less at night? While the adults feeding on leaves can cause a lot of cosmetic damage, uncontrolled larvae feeding on roots are a bigger concern. They can damage enough roots the plant is unable to take up adequate nutrients.

If you want a hands on opinion, taking an example leaf or two to your county extension agent or often full service nursery (not box store) can be helpful....but jean001 is right, that is not a fungal infection causing browning.

I did an Imidacloprid drench around the base of the plant a few weeks ago and applied granular to the rest of the bed to try and reduce numbers of Larvae - I've been out at night a couple times and haven't seen any (first time I went out last summer, I had several on each plant...after a week or two of doing that, I would only have one or two a night, then it was down to nothing that I could see). I will probably do another drench this week, as temperatures warm up, I'm sure larvae are headed up and adults will emerge soon...Beetles are just coming up now (June Beetles I would imagine).

Should I do anything to encourage root growth? How often should I water? I'm nervous to overwater and encourage fungus (even if that isn't what I have now, I don't want to introduce it!)....

I agree it is not a fungus and it is not a problem. It is natural. You have two problems.

1) Wind and cold damage is indicated when the edges of the leaves become distorted and turn brown. This occurs frequently in plants that may be in a colder climate than recommended or in a location with severe exposure. Provide protection from winter winds and winter sun. Note, boron poisoning or fertilizer burn will create the same symptoms except uniformly over the plant rather than just on areas exposed to the sun and wind.

2) Large leaved rhododendrons are susceptible to sunscald if the plants do not receive enough moisture before the soil freezes. The leaves curl in cold winter weather, exposing the central part of the leaf but not the edges, resulting in the area near the main vein becomes desiccated and turns brown. To prevent this, water plants thoroughly before the first hard frost, protect from drying winds, apply mulch, and locate in partial shade.

No disease is evident. The chewing on the edge of the leaves is weevil damage. It is very common in most plantings.

Your nurseryman just made more money by selling you something you don't need.

Part of the problem is fertilizing in the fall. Only fertilize in the spring. Hollytone is a great product, but only use once in the spring and at half the strength recommended on the package. Fertilizing in the fall makes problems such as you have worse.

Only water in hot weather when the leaves are a little wilted in the morning. If you have good drainage, occasional watering will not be a problem.

Here is a link that might be useful: How to grow rhododendrons and azaleas.