"But the Mauder minimum just happens to coincide really really well with the little ice age."
No it didn't, according to the University of Boulder paper the little ice age (LIA) began ~1275-1300 (Mann says is covered 1400 to 1700) and the Mauder minimum only spanned 1645 to 1715.
But I think you're right that the LIA was a false start of a new ice age, indeed the current Milankovitch cycle should be causing global cooling (not warming). Indeed, under such circumstances the climate might be especially sensitive to negative forcings such as volcanic eruptions. Recall, the Milankovitch cycle involves decreased melting of spring-summer ice i.e. it is an albedo feed back that enhances high latitude cooling that causes the ice ages. Volcanically forced increase in polar ice coverage could result in an albedo feed back during this current current
"We don't yet know what causes ice ages"
Milankovitch cycle causes ice ages, Oh, dear.
Mann, M.E., Zhang, Z., Rutherford, S., Bradley, R.S., Hughes, M.K., Shindell, D., Ammann, C., Faluvegi, G. & Ni, F. 2009. Global Signatures and Dynamical Origins of the Little Ice Age and Medieval Climate Anomaly. Science 326(5957), 1256 -1260
Hays, J.D., Imbrie, J. & Shackleton, N.J. 1976. Variations in the Earth’s Orbit: Pacemaker of the Ice Ages. Science 194(4270), 1121 -1132.