"We are flying into AMS for two nights and then heading to Berlin for 4 nights..."
I assume you are not staying at AMS (airport) for two nights but instead somewhere in Amsterdam. If that's the case, then you should probably be using one of the direct trains to Berlin from Amsterdam Centraal - they leave mornings at 7, 9 and 11 am - and that way changes of train and late trains are not an issue. If indeed your hotel and your departure for Berlin are at AMS airport, then you will need to change trains in Amsterdam (if you want only 1 change) or elsewhere (multiple changes.)
Either way you will require a ticket to the German border. Buy it at the station in Amsterdam. Normally your train for Berlin will travel through and likely stop in Bad Bentheim, but there is no reason to get off the train in Bad Bentheim as your rail pass can be activated in advance (see the link provided previously) and is valid once you hit the border.
"We had purchased the Select Pass during the 20% off sale and did the math. It turned out less expensive this way..."
Unfortunately you can't get a complete picture of the non-pass pricing options from rail pass sellers or from Rick Steves' rail pass advice. That math will always be off. I will do the math, using your travel circumstances, in the way the forum "regulars" here would typically do it below, for the benefit of future readers (and perhaps for your own future travels)...
If you are planning day-by-day trips several months out (like the OP is doing) then it's good to look not just at normal prices but at advance-sale prices. These lower prices usually involve train-specific travel - then compare totals to the rail pass option.
The cheapest two-person rail pass in 2nd class that I can find at Raileurope provides 4 days of travel in DE and CZ for $546.
If you bought your 3 travel legs at the German Railways website instead... The cheapest one-way point-to-point tickets in 2nd class at DB, using the same trains you would use on a rail pass, price out at €40, €20, and €15 per person for each of your 3 legs. That's €150 total for two, or $184 total in dollars.