Here is an answer based on photometric arguments: The astronaut probably would not be able to see the rings, but it would be worth a try.
I would recommend the astronaut float somewhere at a distance of ~1.5 $R_J$ from Jupiter's center, where $R_J$ is the planetary radius of 74,000 km (at back of envelope precision). That way, they can look in a direction where Jupiter and the Sun are not in the field of view. You are correct that glare from the planet makes it difficult. This is especially a problem for the existing spacecraft and telescope observations of the rings, because the rings and Jupiter are typically close together in the sky. For an astronaut, that would be a huge problem. The astronaut would want to use some kind of a baffle to block bright objects (like a handmaid's bonnet, but in vantablack). Being at a location of 1.5 $R_J$ puts the astronaut inside the rings, so they can look toward the rings – and away from Jupiter – at the same time.
First we need the solar illuminance at Jupiter, ~128,000/25 lux = 5000 lux (wiki:Lux), because Jupiter is 5x farther from the Sun than Earth is.
Then we need the effective visible area of the rings. I will cheat a bit on the geometry. At 1.5 $R_J$, the astronaut is 0.3 $R_J$ from the highest-opacity part of the ring, near 1.8 $R_J$ (throop++2004, fig. 7). The equivalent thickness of the rings if they were perfectly reflective, called the VIF, is about 4-15 cm (throop++2004, fig. 14). The rings are going to stretch fully across the sky from the astronaut's viewpoint, so I will cheat and say the length is half the diameter of a 0.3-$R_J$ circle. This works out to an equivalent visible area (for fully reflective rings) of 7 km2.
Now we can get the luminous flux of the part of the rings visible to the astronaut, by multiplying the illuminance by the equivalent visible area: 5000 lux x 7 km2 = 3.5x1010 lumens.
The illuminance from the rings, at the astronaut, can be found if we assume each part of the rings is isotropically scattering light back into a half-sphere which has a radius of 0.3 $R_J$. This gives an illuminance of 1.1x10-5 lux, or 0.11 millilux (0.11 mlx).
Would rings with illuminance of 0.11 mlx be visible to the astronaut? The Milky Way gives an illuminance of 13 mlx (NPS), so the rings would be 100x fainter than the Milky Way. This would be pretty hard to see. For comparison, a 6th magnitude star is barely visible and gives an illuminance of 8 nlx (wiki:Apparent_magnitutde). The rings at 0.11 mlx are giving more than 10x more light than this faintest star, but unlike the star, the ring light is spread out in a line across the whole sky from the astronaut's viewpoint. So I think it would be pretty difficult to see the rings, but worth a try.