If I've understood this right the 1.9 edge figure reflects the "BTC In" sum and the 1.9% line on the chart showing pretty flat tells me that 'BTC In' in is also pretty flat. Have I missed something here?
I don't think so. I think you're both looking at much the same thing, in that they're both indicators of the bet volume rather than the (short term) profitability.
The following is the amount of "BTC In" for SatoshiDice.com for four 4-week periods: