In Fig. B circuit I increased the resistance from 1k to 15k and it improves a lot giving small vertical voltage difference of 19mv compared to circuit A with 2.68 volts! The waveform is shown below.
Reducing the charging current further thru the resistor by doubling the resistance from 15k to 30k make it very near linear (yeah almost linear, lol). As you can see from the sim in Fig. C,
Fig. C, Overlaid Capacitor voltage and linear ramp generator are look alike now.
Circuit sim showing reduced charging current using 30K resistor. Then overlaid with linear signal. Now you cannot see the bended one because they are almost identical in linearity. Zooming-in is the only possible way to close examine the vertical voltage difference of the two
There is small amount of voltage difference plotted along vertical axis as small as 4.2 mv which is too small and might be considered benign. See Fig. C.
Peak to peak charging current decreased to 200ua.