Spent my evening unblocking the condensation pump drain line once I realized its overflow shutoff was why my thermostat had stopped getting power. Way too long a run of flexible tubing, and not properly inclined at all. :\
Now have an adapter to tubing for my shop vac coming, as well as what I hope is the right adapter to let me hook up the tubing to my air compressor. Hoping to decisively suck or blow the line clear next time this happens.
Also mulling over any alternative egress for the drain line. A shorter run would be way easier to slant appropriately and to clean out.