Just an update: I was able to purchase 4 train tickets on the DB Bahn site yesterday. 3 of those tickets have reservations.
Ironically, Munich to Berlin--the one trip that should have allowed me to make a reservation, since it's the longest--is the only one that I wasn't able to get a reservation for.
I printed out the tickets, and they're written in German, so it's kind of hard to make out what my seats actually are going to be.
Here's an example (from the Berlin-Dresden leg):

1 Sitzplatz, Wg. 256, Pl. 76, 1 Fenster,
GroBraum, Nichtraucher

I interpret the above as saying that my train's name is "Sitzplatz", and my wagon (car) is number 256. My seat is number 76, and I'm not sure what the rest means.
Can anyone interpret this for me?

I only have one more train ticket to buy: Prague-Vienna. But the Czech site will not allow me to purchase tickets for that yet. I have to wait another 20 days or so.