The shortest hike to reach the designated base camp starts just off BF road below the outhouse before you hit the bridge and heads north (1.5 miles). You can also start at the outhouse and take the official CRT/FHT which meanders a bit before joining the previous trail (2.7 miles).
I have parked at the Fish Hatchery and taken the East Fork Trail down to the same location (2.4 miles). That trail is not quite as easy as the CRT, but it's far from a challenge.
There is also a parking lot near the Fish Hatchery for the FHT which you could take 3.2 miles down to where is joins the CRT plus another 1.1 miles to the group hang (4.3 miles). I've not hiked that trail before.
There is also the option of starting on one of the other Ellicott Rock approach trails from the north and hiking down to meet the group.