If the elm, to begin with, was truly "green", it may well have had >40% moisture content, so let's use 40% as a starting point. In which case your 2.3kg (2,300gm) piece of timber would have been 1380gm of elm and 920 gm of water.
After your drying process, you report that the timber reduced to 1800 gm, given that the only weight lost will be that of the moisture transferred to the desiccant, your "dried" piece would have been 1380gm of elm (as before) and 420gm of water, thus its new moisture content would have been 23%.
Using these figures, when your wood eventually reduces to about 1560gm, it will be 1380gm of elm and 180gm of water, which equates to about 12%mc. This suggests that you keep drying until your piece weighs about 1560gm.
Admittedly, these figure are based on a few assumptions, but should be a fairly good guide, and it serves to stress the point that even if you haven't got a decent moisture-meter, when working with green timber you can calculate useful data based on weight loss.
Les