A rigid ceramic refractory base for a single-stack annealing furnace is assembled atop a base support structure utilizing a novel set of cast refractory segments, including a pair of C-shaped inner segments and four arcuate outer segments. Defined between the assembled inner and outer segments is a circular inner seal positioning trough that opens upwardly, and that has a tapered cross section that narrows with depth. A resilient but reinforced inner seal of novel form is installed in the trough utilizing upper and lower blankets of refractory fiber material that sandwich a plurality of elongate refractory fiber modules arranged end-to-end to circumferentially fill the trough. Each of the modules includes a serial array of compressed, cube-shaped blocks of fiber refractory material that are interspersed with thin, perforated metal members, with each of the arrays of fiber blocks and metal members being held together to form a module by metal rods that extend centrally therethrough and are welded to perforated metal members that cap opposite module ends. Arcuate steel structures that are assemblable to define an outer seal positioning trough are anchored to the cast refractory outer segments during their fabrication, and have end flanges that enable the cast refractory outer segments to be securely bolted together during assembly of the base. Associated methods of fabrication, assembly, use, maintenance, repair and replacement are disclosed.