I think the way to settle this would be to find out from OP what the failure modes are. He never specifies whether he just gets back pure starting materials, or if he gets his amine back, but the 1-methoxy-4-methyl(1-ethoxy) benzene compound is present.
Rotovapping it down and NMR of the crude should give it away, the benzyl peak will shift, while the piperidine will stay the same if there is ethoxide attack. You can do a HCl extraction to remove the any version of the piperidine from the crude if its too messy to interpret.
PS If there was a strong base like KOH in this, I'd expect aldol condensation of that ketone to occur.
PPS pgk I think you are thinking of using K2CO3/MeOH for TMS-alkyne hydrolysis. Its a way to avoid fluorides or acids when deprotecting those compounds http://cssp.chemspider.com/article.aspx?id=100
In respect to the paper you cited, ester chemistry is much different from the irreversible reaction we are talking about at the benzylic position. Catalytic base and a huge excess of a MeOH can cause transesterification. You are transesterifying that acetate to give the alcohol and methyl acetate in that paper.