The small stream is called Carillon Creek. Because a few mistake this for the North Fork of LP Creek, a use trail up it has gradually become worn. I’ve ascended it twice, heading for your canyon east of Carillon and south of Peak 12,960+ (known locally as Gambler’s Special Peak; more on this later). Going up is somewhat tedious due to the brush you mentioned. I like the approach to this canyon from the slopes above Lower BS Lake much better.
For the descent, however, going down via Carillon Creek to the main trail is straightforward and quite a bit faster than the regular NF trail. With the aid of gravity, the brush is not a problem.
There are at least three reasons people go into this canyon. One is to climb Gambler’s Special (cl. 2) and another is to gain the difficult rock routes on Carillon and the Cleaver (13,355’). A third is to go over Carillon-Cleaver Col to Tulainyo Lake. This col is a more direct way to Tulainyo Lake than Russell-Carillon Pass and is 400’ lower, although it is terribly loose in spots – dangerous, even. It is also called Suicide Col. It is much nicer in winter and spring, with snow coverage. A rope may be useful.
Why the name Gambler’s Special Peak? On February 18, 1969 a DC-3 returning to Burbank from a gambling outing in Hawthorne, NV, in a snowstorm, turned up missing. The plane, with 35 aboard, was called Gambler’s Special. The search for it was unfruitful.
Then, on August 9, the wreckage was spotted from the air. The plane had “slammed into a sheer rock wall” on the NE side of this peak. The wreckage sighting was reported the next day on the front page of the LA Times, right under the grisly announcement that actress Sharon Tate and four others had just been found murdered. Tate was 8 months pregnant (her husband was film director Roman Polanski); Charles Manson and his friends were subsequently caught and convicted of these and other murders.