Both transistors have a minimum gain of around 80. Changing those is unlikely to make any significant difference.
The base drive current is more likely 8 - 9mA, which gives over half an amp switching capability.
(the actual base current is set by the voltage across the 470R base resistor; 5V less the 0.6V or so base-emitter voltage of the transistor and less the slight positive voltage on the PIC output when sinking that current).
The LED current should be (5V - (ULN2803 voltage drop + LED voltage drop + anode driver drop)) / 47R
The voltage drops will be anything from around 2.5V to 4V or so, depending on the LED colour etc., so current (2.5 / 47) = 53mA down to (1 / 47) = 21mA
With 1/16th duty cycle, the equivalent average currents are 3.3mA down to about 1.3mA, which is likely why the LEDs are dim.
For 1:16 multiplex you can use LED current MUCH higher than the continuous current rating of the LEDs, as long as it's below the short term maximum.
The LED data sheet should give the required info, or post the LED type number so someone can work it out.
A resistor change is probably all you need, you have everything else working OK by the sound of things.
(Though thinking about it, you may need to keep any eye on the driver devices to ensure they are not getting too hot, with higher current through multiple LEDs).