Your multimeter probably won't give you an accurate reading for the voltage across R3, because of the waveform. Forget that reading.
If you want to keep with 18 LEDs but increase the current, then make C1 = 330nF (X2 rated, >250VAC), R3 = 1k2 (1Watt rated) and C2 = 100uF (100VDC). The LED current will then be ~18mA average, peaking at ~27mA (which is close to the probable safe limit to prevent burn-out). The brightness won't be much greater than now.
If you add more LEDs it will be more power-efficient to connect them in series with the existing LEDs rather than in parallel.
Here's a suggested circuit with three strings, each of 18 LEDs, in series. Note that C1 is now 470nF (0.47uF), X2 rated, >250VAC.
R1 is 470k (as you mention above), R2 is also 470k, R3 is 1.2k but must be rated at at least 1 Watt.
C2 can be 47uF, but its voltage rating must be > 200VDC.
Don't expect a huge increase in the apparent brightness (because of the ~ logarithmic response of the human eye).
Be aware that all parts of this circuit are potentially at a lethal voltage and due care must be taken in building and using it. Don't go ahead unless you appreciate and accept the risk.