Embodiments of a turbine nozzle assembly are provided for deployment within a gas turbine engine (GTE) including a first GTE-nozzle mounting interface. In one embodiment, the turbine nozzle assembly includes a turbine nozzle flowbody, a first mounting flange configured to be mounted to the first GTE-nozzle mounting interface, and a first radially-compliant spring member coupled between the turbine nozzle flowbody and the first mounting flange. The turbine nozzle flowbody has an inner nozzle endwall and an outer nozzle endwall, which is fixedly coupled to the inner nozzle endwall and which cooperates therewith to define a flow passage through the turbine nozzle flowbody. The first radially-compliant spring member accommodates relative thermal movement between the turbine nozzle flowbody and the first mounting flange to alleviate thermomechanical stress during operation of the GTE.