The US passport is not so bad in this case. Yes, for China visa it is $140 whether for single, double, or multiple entry, but for Mongolia, US citizens get in free for stays up to 90 days, which should be adequate for a scouting mission. If you are resident in Cambodia, go for the double-entry Chinese visa, definitely, and ask for 60 days duration of stay per entry to give you greater time options, even if you end up not needing this much. I do not think you will be able to get a 12-month multiple entry visa in Cambodia--which is standard issue to US citizens if applying in the USA.
From Bejiing to the Mongolian border, you have 3 options, each will cost you about US $30-33 excluding food on the journey and any accommodation or costs you expend if you stay in Beijing (which you probably should plan on).
1) K3 or K23 train Beijing-Erlian. Timing of train requires an overnight in Erlian. Downside: only runs on certain days and ticket purchase requires very specific procedure, best documented in this thread , which you should read and thoroughly digest. Approx $23 train and $10 night in Erlian = $33
2) K573 train Beijing-Jining South (Jiningnan) overnight, then switch to public bus to Erlian. This has the advantage of being a daily and purchaseable at any ticket office without special procedures. Timing is 20:45 -05:00 into Jining Nan. There are other trains doing this route but the K573 has the best timing for what you need. Not sure timing of earliest bus Jining-Erlian but probably about 07:00 am, which would put you in Erlian around 12:00 noon. Hard sleeper US $20 + bus $11 = $31
3) Sleeper bus Beijing-Erlian. Timing is usually about 17:00-05:00. Have to kill a bit of time in Erlian before border opens. Advantage is easier to get a bus ticket a day in advance than a sleeper train ticket. Cost about $30.
Add to that: $7-10 to get from Erlian to border then all the border formalities and into Zamyn-Uud. About $27 hard sleeper Z-U to UB. So yes, BJ-UB can be done for about US$65 plus food.
The biggest determinant of your travel cost and time is going to be how you get across China. For current details and pricing on overland through Laos, ask on the SE Asia board. I believe all things considered, going through Laos and heading for Kunming will be cheaper than going through Vietnam. Do not use kayak or any other western site for China domestic airfares. Try www.ctrip.com or www.elong.net or www.travelzen.com and remember that domestic airfares in China are often most heavily discounted 2-6 weeks out, not months in advance which may show only full fares. Doesn't really matter which domestic airline you use, but go for a nonstop.