Scaling voltage to meet two conditions at once
What are some ways I can accomplish this?


Using an offset and a gain, \$V + A(V_{battery}) = V_{CC} \$, the equations are:

\$V + A(3.45V) = 3.1V \$

\$V + A(3.55V) = 3.3V \$

The solution is:

\$ A = 2, V = -3.8V \$

This would be straightforward to implement with a simple opamp circuit.  I can post one later if you're interested.




  Also, really, I'm just interested in the academic value of knowing how
  to do this kind of linear voltage transformation generally speaking


Here's a circuit fragment to illustrate the basic idea.  This should get you started.