Can 4-pyridones be synthesised analogously to 2-pyridones?
A reliable and old reference on the synthesis of 1-methyl-2-pyridone (Org. Synth. 1935, 15, 41, DOI) does not mention the formation of 1-methyl-4-pyridone as a side product and I doubt that it and can be formed that way.

The synthesis of 1-methyl-2-pyridone starts by reacting equimolar amounts of dry pyridine and dimethyl sulfate to form the N-methyl pyridinium salt. Then, the mixture is diluted with water and solutions of $\ce{NaOH}$ and $\ce{K3[Fe(CN)6]}$ are simultaneously added.

This seems to do the trick: the $\beta$-amino alcohol formed by adding $\ce{OH-}$ ortho to the nitrogen atom is immediately oxidized, which prevents the opening of the pyridinium salt.

For the synthesis of 1-alkyl-4-pyridones, a somewhat classical approach would be to react the corresponding 4-pyranone with a primary amine under more or less drastic conditions, as shown in Can. J. Chem., 1976, 54, 3377. 

Altenatively, Grignard reaction of a 2-substituted 4-benzyloxypyridine-N-oxide, followed by debenzylation/methylation with methyl triflate and subsequent treatment with $\ce{NaOH}$ will yield the desired a 1,2,5-trisubstituted 4-pyridone (DOI).