I do wonder why people feel they need to use these "organized" trips. ...
...Try on your own, you certainly will not regret doing so
I'd second that having just returned from my third trip to the area in the last three years.
There are plenty of hotels handy for public transport in the area; I've always stayed in Wernigerode.
Aside from traveling on HSB, the hotels will give you a booklet of discount vouchers which also allow free travel on most service buses in the Harz region.
Last year I had a longish stay in the area starting in Nordhausen then travelling on to Wernigerode using the remarkably good value HarzTourCard which at 18 (the same price as a single from Nordhausen to Wernigerode) is valid for three days on all of the HSB (except Schierke to the Brocken) plus buses and some DB and HEX trains.
I spent the other two days on the Harzquerbahn and Selkatalbahn and then got a three day ticket for the HSB to do the Brockenbahn.
To be fair, RTC's tour does include the Rübelandbahn and a bit of main line steam but I'd rather have the flexibility and avoid paying almost £2000!