Well I didn't have much success with these encoding formats. I've tried both RGBE and LogLuv, both of which exhibit numerous problems.
The first problem in my implementation is that both RGBE and LogLuv display thin bright rings at certain edges along the bands (which is another problem). The problem appears related to linear filtering, since disabling that fixes the issue. I'm not exactly sure why that is an issue since logically both formats encode data in a way that is filter friendly. The encodings also appear to be destructive, as you can see in the image the surface of the sun appears altered, more so in the LogLuv implementation. The banding is definitely an issue with RGBE. Larson even admits that it's a potential problem due. LogLuv does a fairly decent job at reducing the bands, but it suffers more from discs appearing in the image. You can kind of make out the disk in the image, but it's more prevalent when you increase the exposure.
To be on the safe side, I assumed I misinterpreted Larson's paper or his algorithm. So I tried a couple other implementations I found scoured on the Internet. I found an optimized version of the LogLuv formula
here. Interestingly, this version does not suffer from the rings I was getting due to linear filtering, but it suffers horribly with banding and discs, far more than my "true to the paper" implementation. At some points it looks like you're staring down a discrete multicoloured tube.
Now I have tried the algorithm on standard gradient images and they do appear fine, so I'm wondering if perhaps atmospheric scattering falls under the exception to the rule. Perhaps the dynamic range requirements are stretching the capabilities possible with just 32 bits? I don't know, but I'm losing faith here