I found a few photos and I think that HD tail lamp presents a problem using the kind of conversion that you're looking for. It looks like the tail light uses one double contact bulb to also illuminate the license lamp. If you use Red LEDs, your license will illuminate Red, which could attract unwanted attention from those pesky law enforcement officials.
If you use White LEDs, your license will light up fine, but a red lens just about drowns out any light from a white LED from coming through, so you would lose your tail light. I found ready made a 90 deg 1157 conversion that might work, but you would need a voltage booster in the lamp housing to kick it up to 12 volts and you would still have no license illumination. That fixture may require two separate custom conversions within the lamp housing; Red LEDs for the tail/stop and white LEDs for the license, each fixed in different directions.
I don't know what a Monarch lamp looks like yet, so I'm not sure if it would present the same problem as the HD tail lamp.