Unless you know your plans are certain and can buy your ticket one year prior to departure, then it will often be cheaper to upgrade onboard.

All Amtrak sleepers have 5 different pricing levels or buckets. Except during peak travel times, a room will start out at the lowest bucket. The prices between buckets can vary by as much as $200. Once a few rooms start selling, Amtrak starts kicking the bucket up to the next level. This trend continues as more rooms sell, till the highest bucket is reached. Typically when about 75% to 80% of the rooms are sold, you can expect to pay the highest price.

Again it should be noted that peak travel times can vary how fast the top bucket price is reached.

Now, if one upgrades on board, then one will always pay the fare of the lowest bucket for your upgrade. Of course the risk is that there will be no rooms available by the time you go to travel. Especially on certain routes and during peak travel times. So it's a gamble to wait until the last minute.

But if lowest cost is most important, then the rule is either book as soon as ticket go on sale (1 year before the start of travel) or wait until onboard to guarentee the lowest price and hope that they aren't sold out.