I have done this route twice in the opposite direction, from Thousand
Island Lake
to Twin Island Lakes.
It's a steep drop from Lake Catherine
to Twin Island Lakes (for you, a steep climb). I took this photo at
Twin Island Lakes looking up toward Lake Catherine. Mt.
Ritter appears in the upper-right of the photo; I think that's peak 3518-7 on the left. You can make out a stream in the middle of the photo. I can't imagine following that stream down or up, as Wandering Daisy suggests, although she is much better mountaineer than me and for all I know you are too.

- View looking east from Twin Island Lakes to Mt. Ritter
You will have
to do a lot of talus hopping no matter what. From the point of view of the northern
Twin Island Lake, go north up Roper's "U-shaped" valley (north east of the Northern
Twin Island Lake), and then head toward his "reddish cliffs." From there, contour your way around (south of) peak 3518-7. The terrain gets more forgiving (less talus, more green plants) the closer you get
to Lake Catherine. In this route, you stay north of the stream and the cliffs and sort of circle your way up.
This is the view from the head of the "U-shaped valley." The trail from Hemlock Crossing ends at the bottom of this canyon.

- Head of Roper's "U-shaped canyon"
Here is the view of North
Twin Island Lake that you'll see after you climb a few hundred feet above the "U-shaped canyon":

- View looking east from Twin Island Lakes to Mt. Ritter
It's easy
to find North Glacier Pass from Lake Catherine, and the hike down
to Thousand
Island Lake is easy
to navigate, since you can see the lake from the top of the pass.
Inbox me if you want more info. BTW, have you considered adding Bench Canyon
to your trip? There isn't much snow in the Sierra this year, so you can cross the North Fork of the San Joaquin above Stevenson Meadow and get
to Bench Canyon. I took the trip last year (I wrote a report about it here:
viewtopic.php?f=1&t=8190" onclick="window.open(this.href);return false;). It's about a day trip Bench Canyon
to the
Twin Island Lakes.