Under Directive 2004/38/EC, the residence card is so called, rather than being called a "residence permit," because it serves merely as evidence of your right to reside in Germany as the spouse of an EU citizen. The right exists independently of the document, solely because you have moved with your wife to Germany. Because you are staying in Germany as a family member of a union citizen, you are not subject to the limitation of 90 days in a 180-day period, regardless of the fact that you do not yet have your residence card.
You should therefore be able to enter the Schengen area with evidence of your marriage and that your wife is an EU citizen resident in Germany. To that end, you can travel with a certified copy of your marriage certificate, a certified copy of your wife's passport or national identity card, and a certified copy of some document showing that she resides in Germany.
You may be asked to prove that you are either traveling with her or joining her wherever she may be in the Schengen zone. The first will be easy to prove if it is the case, of course; for the second, you may want to have her on standby with a mobile phone at the time of your arrival and departure.
In practice, since US citizens enjoy visa-free entry into the Schengen zone, you will only need this evidence if someone tries to fine you for overstaying in the Schengen zone, to show that you are not subject to such a fine, or if someone tries to deny entry, to show that you are not subject to a denial of entry on those grounds. More likely, you'll just be allowed in.
Strictly speaking, as a "person enjoying freedom of movement" under the directive, you're allowed to use the "EU passports" desk when you arrive in a Schengen country. If you have all those certified copies I mentioned, you might give it a try. Otherwise, I would probably just use the "all passports" desk and only bring up the freedom-of-movement angle if it seems appropriate based on the questions you're asked by the officer.
To address the scenario in your question, if you apply for entry along with your wife, and in possession of a copy of your marriage certificate, there is no way they can deny entry except on grounds of public safety, public health, or public policy, regardless of how many days you've spent in any EU or Schengen country.