Unless one likes to play the role of shipping agent right around the time of a trip, a better solution is to transport via a company which specializes in such affairs, like Luggage Forward. For a flat fee based on weight and size, they will pick up and deliver from your home/office/etc to your destination (hotel, relative, etc). Discounts are offered if you drop off yourself and for a less speedy delivery (eg, ground vs air). Depending on who the current contract is with, the actual carrier will usually be FedEx or UPS. In most cases, delivery is timed to your choice of arrival dates, with limited guarantees (subject to carrier delays, etc). Since they perform their own internal logistics, this is often better than you can do on your own with the carriers (unless you are shipping through a company with a contract they wish not to lose), and gives an additional layer of assistance. Rates are usually less than excess baggage fees through the airlines, though sometimes can be more, though the trade-off is that luggage transport companies will usually move items the airlines won't so long as the items meet the carriers' guidelines.
It's under the 75" linear inches for checking in. I doubt you'll have any problems getting it to fit in a rack and really surprised if they whipped out a tape measure. There are of course the sizers at some stations, but that's really for the passenger to use. I'd be surprised if they did anything as long as that's all you have.
It really depends on the station. A lot of the smaller staffed stations basically have one employee at a time to do everything. It may get somewhat quiet for a while, but then everything is heaped on that one employee at the same time. I was at one of those stations and asked her how they're scheduled. Apparently it's two employees per station with staggered dates and times. A lot of these stations will have one train in each direction per day, and depending on the schedule, the employees will work one long or two two short shifts per day, which may include early morning hours. If it's a long shift there may or may not be a lunch break listed in the hours. Once the train arrives, the single employee will need to leave the ticket window and handle the baggage.
I do the same, UPS. I mail about a week ahead and the boxes arrive when I do. I take a lightweight carry on and my laptop case. Dislike dealing with a lot of luggage on the train. I really dislike paying airlines to handle my luggage. To me its the same amount of trouble going to UPS as checking in bags. If one plans a head the procedure works really well.
Short - checking can work out if it's reasonable for you to drive or get a ride to the station your bags are checked to after you arrive at your "real" destination... but don't plan on claiming your bags and then re-boarding the train! If you ever do short-check, be sure to check station hours... many staffed stations close immediately after the arrival of the last (only!) train of the day. You could try to come get them during business hours the next day, but a storage fee may apply if you wait more than 24 hours.
Might be possible depending on the station and the personnel. I wouldn't count on your plan working though. Some employees might be required to take it to the baggage room. At some stations the baggage cart is taken to a bus loading area where bus transfers are made, are claimed on the spot, or go to the baggage room if they're unclaimed there.
You said that your bag was 30"x20"x14". If that's correct, it is technically oversized as Amtrak carry-on is limited to 28"x22"x14" where it theoretically has to fit in a sizer like this one:
