Circuit to boost PWM voltage using ULN2803a
Can I suggest you use a ProFET high-side driver IC. These devices give you a switchable high-side drive with protection from all sorts of things, including output over-current.

You can find and select ProFETs readily enough in distributors. If surface-mount is awkward for you, I'd recommend the BTS50080-1TMB Smart High-Side Power Switch in a TO220 7-lead package. You can drive its control input directly from your ULN2803 outputs. Its output drives your LEDs with your 10 V or high impedance for PWM driving.

If surface-mount parts are no problem, look at the BSP752T which is cheaper, smaller and can be driven directly from 3.3 V or 5 V logic rather than through the ULN2803.