Okay, guide me on this. Assiniboia presents 16 times the surface area as seen from Regina, but Assiniboia is from 8.5 to 17 times farther away, reflecing light that in that orbit is roughly similar to what we receive here on Earth. So, if Assiniboia's farther away, the light reflecting from it travelling farther to reach Regina, does that not mean it's not as bright? I'm still seeing the night as dimmer than on Earth, at least with respect to the reflected light from Assiniboia.
Assinoboia presents well more than 16x the actual surface area. It presents 16x the angular area, being 4x the angular diameter. Or more. depending upon where it falls in the "how big is «bigger than 60,000 km radius»" ... but that doesn't matter for this because the apparent diameter remains the same whatever value we pick, because it's 55/2 times that distance.
We'll come at it the other direction...
luna is 3340km diameter - vs at least 120,000 - roughly 36x the diameter, and thus at least 1291x the area. Regina is 3,300,000 km out, while luna is 345,000 or so. 9.5x the distance, roughly. 1/91 as much of the reflected light arrives. 1291/91 is around 14.2x the light.
Also, a gas giant is likely to have a higher albedo (luna is .12 average) while gas giants in our system have albedos in the .25-.35 range. Thus double or triple the illumination factor. so 28-42x the brightness of a full moon on earth.
Plus, a companion star.
1/4 the year, the companion lights the dark night when between 135° and 225° orbital position (assiniboia→primary = 0°), because during that quarter, the companion is in the same 90° arc from assinoboia, and thus opposes regina. Probably about crescent moonlight level.
True darkness is only at opposition, during the nights when outside of assinoboia.
And don't forget - assinoboia, being at least jupiter sized, radiates compression-generated IR. Gonna be fun-warm.