I registered my initial skepticism about Matthean posterity here. However, Paul Davidson has made his case for Matthew’s use of (proto) Luke with examples such as the parable of the talents/pounds, the Beelzebul controversy, the golden rule and command to love enemies, and the Lord’s Prayer. I am not persuaded by the efforts to reverse the line of influence from Matthew to the Didache (note that the “Gospel” references have to be judged as a later layer) and I will follow this up with a post on why I think there are grounds for extreme caution before admitting Marcion’s Gospel into the Synoptic Problem. However, check out his well written posts and see if you are persuaded by his case.
Alternative Synoptic Solutions: Matthew as the Last Gospel Part II