mike27oct: My knowledge of home audio is patchy at best, but I believe most of those 3.5mm stereo to 3.5mm mono "converters" actually only take 1 channel (left or right): if you plugged a headphone into it you would only get sound in 1 ear. What I am proposing is to short L+R, before feeding it into my amp; which according to various online sources does carry some risks (device-dependent).
Ideally the Echo Dot would be able to do this in software (as my android phone can), but since it doesn't seem to be able to, I am left with this solution (cheap but potentially dangerous to the dot), or buying a converter box that does this (and realistically, I would just buy another amplifier which has this feature built-in as yours does before I did that). But I won't buy another amplifier: if this can't be done on a shoestring it won't be done at all.