It is difficult to explain why this reaction is giving the products found, however one cannot overlook some factors. Even though a Claisen condensation of an ester can be catalyzed by an alkoxide, the reaction must overcome a big kinetic hurdle as alkoxides are much less basic than the ester alpha hydrogens. Consequently, the alkoxide and ester should match to mask ester exchange.
In this reaction, using an alkoxide with a vinylog of an imide increases the carbonyl reactivity compared with a simple amide. Since the isolated products are the cleavage products, the reaction is occurring at the carbonyl group. Furthermore, since two carbonyl groups are present, I am uncertain whether reaction is occurring at the desired center.
Changing the R-group could increase the alpha hydrogen acidity. Certainly other strategies could also be successful by an initial reaction on the "ketonic" carbonyl group and a secondary amide bond formation.