Without a datasheet, nothing is certain. But Sanyo do seem to be masters of the art and tend to lead the field in LSD NiMH. Their claim for a 1500/2000 cycle lifetime (eneloop / eneloop lite) and 75% retention at 3 years is superior to anything else I've seen so far. They also claim operation at down to -20 °C. No curve shown but liable to be acceptable given -10 °C curve.
So, I'd expect that you may well get inferior performance from other brands — especially from those who provide no datasheets.
It sounds like you may have a handle on your question already, but I would like to add a couple of points about NIMH vs Alkaline.
You don't say how many watts or how many amps or milliamps your megaphone will be demanding, but the NiMH have a much lower internal resistance and so they can provide a much higher current without dropping their voltage as much as an Alkaline will. At higher loads, a Nimh will provide more power than a Alkaline; at very low loads, an Alkaline will provide more power (a very very loose generalization, but for example, an Alkaline will last forever in a remote control while the NiMH will not last as long - of course there is also the self discharge of many of the NiMH).
Also, most NiMH have a NOMINAL volatage of 1.2, but fully charged they start out at closer to 1.4 (I have measured some NiMH fully charged at 1.5) volts, and as mentioned already, hold to the 1.2 volts for most of their discharge.
The Alkalines often start closer to 1.6 volts, but quickly lose voltage as they discharge so that their average voltage through their life is about 1.2 Volts! Of course this depends on what the cut off voltage of your Megaphone is.
Don't forget that most NiMH have a very high self discharge rate and can lose 10-20% of their capacity in the first day, and 1% of their capacity per day just sitting there and are essentially completely discharged in 3 months or less! There are newer NiMH that hold 85% of their capacity over a year.
Check out http://batteryuniversity.com/learn/article/Nickel_based_batteries for more info.
As far as your 4 options, option 2 sounds like the best one. Options 3 and 4 have been discussed by others as to why they offer such poor performance.
Best Answer
The answer is: marketing. Some number, like "1800 mAh", doesn't really mean anything, anyway. At what temperature? At what voltage is the battery considered "dead"? At what current? The charge you can get from any type of battery really depends on these factors, and how far dead you are willing to run it.
All the major alkaline battery manufacturers supply datasheets that specify the capacity of their batteries more completely. This is the place to get capacity information, not the product label.