Hi
Ruth is right that this is not a common route by most travelers.
The locations you have mentioned are the popular locations near Dalanzadgad that are well known to all tour operators.
The route from Sainshand offers beautiful locations on the way to Dalanzadgad, some are less known.
If your tour is mainly to the popular locations near Dalanzadgad, I would suggest you stick to the regular route going from UB.
If you are adventurous (it seems so from your post) and want to explore the less known route from Sainshand - so here are some details.
You ask: get off the train in Sainshand
Yes the trains stops at Sainshand.
You ask: if this is possible?
Yes there is a very nice desert dirt road going across the Gobi all the way from Sainshand to Dalanzadgad (where the more popular tourist attractions are).
You say: looks like a beautiful part of the Gobi
Yes indeed this is a very nice part of the Gobi which is overlooked by tourists and most tour operators.
You say: stopping on the way to see whatever there is to see
Just to mention a few -
The renewed Danzan Ravja museum in Sainshand
Danzan Ravja (1803-1856) was one of the greatest intellectuals in Mongolian history, he is little known in the west.
He was a skilled artist, talented composer, leader, educator, play write, reformist, astronomer, architect, healer, and founder of 11 institutions and monasteries across the Gobi. The museum displays some of his works unearthed in the Gobi desert where his treasures where hidden for 60 years in crates, to protect them from the communist regime in the 1930's.
Tavan Har (Tabun-Khara-Obo) Impact Crater
A perfect circular crater created by the impact of a meteorite, it reminds images of the moon surface.
Kamariin Khiid monastery
Founded by Danzan Ravjaa in the Gobi, destroyed during the Communist purge in the 1930's and now reconstructed.
Near by is a reconstructed shamballa, hermit caves, remains of the first Mongolian theatre, large Ovoo in the shape of a woman's breast.
Demchig Khiid Monastery
Near Khanbogd, in a location named the Golden Pita, and by Buddhist's "world energy center", which is also the name of a tourist ger camp near by.
There are also remains of petrified forests in various locations along the way from the times that dinosaurs roamed the jungles in this area.
The challenges
Time
You say: spend about a week in Mongolia
The distances are long on difficult desert dirt roads. You might want to plan for longer to avoid driving long hours every day.
Accommodation
You can camp out if you bring the proper equipment.
A low profile hotel is available in Sainshand, khanbogd and Dalanzadgad.
There are a few tourist ger camps on the way to Kamariin Khiid, and one near Demchig Khiid.
October
You say: mid-October 2009
October marks the end of the tourist season, and the beginning of winter.
It will be cold at night, and not warm during the day.
Some of the ger camps might be closed as it is not high season.
Cost
You say: join me to lower costs
Depending on how many partners in your group expect about $60 - $90 per person per day for a shared jeep, and $70 - $120 with a tour company.
Finding a driver
Most tour companies and guest houses will offer to send a driver to Sainshand to wait for your group if you pay in advance.
You can also find drivers in Sainshand that will be happy to take you, but the chances of finding an English speaking driver in Sainshand are low.
Links:
Danzan Ravjaa treasure hunt published on ToMongolia
Danzan Ravjaa and Khamariin Khiid published on Mongolia-Web
Map of Sainshand and Khamariin khiid area on Google maps
Zoom in to the maximum and change to Satelite mode to see full details.
List of all Mongolian tour operators on ToMongolia
A 12 chapter story with pictures about a hike in the Golden Pita published on Mongolia-Web
Have a great trip
Dan