My understanding is that when demand is elastic, a price reduction will increase total revenue.
Some readers may want to know that an elastic demand can either be unitary elastic ($E_d = −1$) or relatively elastic ($−∞ < E_d < −1$). When unitary elastic, the above statement is not true, strictly speaking.
Can anyone reconcile this with the point that when demand is elastic a price reduction should increase total revenue?
Actually, to be logically compatible with your "point" (in which the observed change in total revenue is the objective reference of accuracy), your elasticity should be smaller than $1$ (in absolute value). Which you do not get since you are using an approximation formulae, not good enough in this case. Indeed, as outlined in the other answer, this approximation formulae is only good for infinitesimal changes.
That being explained, note that the mathematical construct behind elasticities is based on continuous sets. A better approximation is then
$E_d = \frac{\ln(1240/1000)}{\ln(80/100)} = \frac{.215}{-.223} = -.964$
so $−1 < E_d < 0$, which caracterizes a relatively inelastic demand. In this case, as summarized on wikipedia, when the price goes down, the total revenu decreases... which is what you see. Put differently, the "reconciliation" you are searching lies in the fact that you are actually not dealing with an elastic demand.
NB: The better approximation
here lies in computing variations as
$\left[\ln\frac{a}{b}\right]$ instead of
$\left[-1 + \frac{a}{b}\right]$. See
this answer of mine for explanations.