Thank you, Dave, for your question and especially for your inspiration for this post! You raise a good question about the possible influence of climate change. First, I want to mention that our dynamical seasonal prediction models do incorporate the effects of climate change both directly from the prescribed greenhouse gases and aerosols and more indirectly through the global sea surface temperature patterns that result from their influence. So, in principle, if the effects of climate change are significant and if our models capture the effects correctly, then we would expect to see some divergence between the analog-based and dynamical model guidance. Clearly, we do see such divergence when we look a more thermodynamic variables like surface temperature (effect of the long-term trend), but the dynamical effects seem to be more subtle and uncertain. 

This is a topic that a number of research groups have been investigating. One of the earlier studies of which I am aware which was coauthored by fellow blogger Michelle is Kumar et al. (2010). That study argued that the sea surface trend in the Indo-Pacific warm pool had been altering the La Nina teleconnection (some interesting similariities between the teleconnection trend in that study and the observed pattern this year west of Alaska). Since then, there have been numerous studies on the projected changes in ENSO teleconnection patterns (Tom covered one such study here). It's an important question that still needs a lot of answers.