Sounds like a network issue. Do you get this issue when playing offline with bots?
Have you got netgraph ('net_graph 1' in the console) turned on? Should give you some diagnostics. When you get stutters and lag does it change at all? Like a non zero loss% or choke%? I know you said you have no packet loss but your problem sounds like it's stemming from a network issue so its best to double check.