Based on your claims my dear friends these two sentences could be correct :
1. That was a strikingly convincing argument that the speaker delivered. ( strikingly modifies the adjective "convincing" or " the verb " delivered")
2. That was a striking convincing argument that the speaker delivered. ( striking modifies the noun " argument" )
Am I right?
You have the basic idea. The adverb modifies "convincing," not "delivered."
I still want a comma if you want to use two adjectives like that together.