I've added an op amp preamp configured for 10 dB of gain and ordered a set of boards. 10 dB is ostensibly too much gain, but the way things are now, the two gain pots are all the way up. With 10 dB of intermediate gain, the hope is that the "sweet spot" for the output will have those pots further down in their ranges. The most likely explanation I can come up with is that the maximum amplitude of the output from the controller is 1.65Vpeak. Doubling this yields 3.3Vpeak. If you calculate the average power (P = Vpeak^2 / 2R) into 8Ω, you get a little more than 0.5W. If instead you look at the power from 5Vpeak, it's over 1.5W.

Configuring an OP Amp for a single supply voltage to amplify an audio signal isn't too hard. You use an inverting configuration (because audio doesn't care if it's inverse - that just means the speaker pulls instead of pushes, but it sounds the same) with a Vcc/2 virtual ground (classically the non-inverting input is grounded) made with a two resistor divider (and a decoupling cap). The input and output are both AC coupled. The LM4871 generates differential output power with 3 dB of gain, so if the output of the pre-amp is maxed out, it will max out the output of the power amp.

I've now got two choices for speakers. One is smaller, but it's low frequency performance is much poorer (as you might expect). It's also a couple of dB less efficient overall.

If the result still isn't loud enough, then the audio amp will need to be ramped up, probably to something running on a higher voltage supply.