I am about six months late to the party, but for what it is worth, here are my comments.
I too have adopted the BME280 as my device of choice for the time being. It is more expensive but when only buying a handful for myself that is fine. Your considerations for emonTH are inevitably more complicated. In my tests which you have already seen (http://www.kandrsmith.org/RJS/Misc/Hygrometers/calib_many.html) it gave the most accurate results, particularly in terms of thermal and long term stability. Some of the others were great at a certain temperature but then drifted when the temperature changed. I am a little nervous making that statement publicly because I can only speak to the specific devices I tested, not the average device off-the-shelf. Also, when I look at my SHT71 data (http://www.kandrsmith.org/RJS/Misc/Hygrometers/calib_many.html#results_ht) the humidity vs temperature plane is extremely ‘flat’, in fact just as flat as the BME280. The problem is that it is tilted so on the basis of this one device the BME280 definitely wins, but one tiny tweak to the internal calibration parameters could fix it and make it just as good. Was I unlucky to get a bad one? I have no idea. Mind you, the SHT71 is even more expensive still and does not have a barometer so I still favour the Bosch device. The BME280 also has a variety of options for internal filtering and averaging which is all very nice.
On the temperature accuracy, the data sheet does as you say caution that they do not really consider the device to be intended for precision temperatures, but my tests have looked perfectly fine for my needs. I must stress this is just my own “home made” experiment, not based on proper lab certified references or anything, but the six BME280 I tried gave errors of +0.3, -0.1, +0.7, +0.2, 0.0 and -0.5 deg C. The write up, if you are interested is here:
http://www.kandrsmith.org/RJS/Misc/Hygrometers/absolutetemperature.html