My speed, both sprinting and natural cadence goes up when I lift. I lift until the end of April, and then do maintenance lifting during May, then quit. Lifting really does put a training load on a person, doesn't it? In a way, that's good, because it's like adding mileage. Builds base.
You could try adding fastpedal (115-130 cadence) for 15-45 minutes during your recovery rides. You are doing recovery rides, right?
But why are you talking to us? You've got a coach. Hopefully he/she has a track record with other cyclists you know. Either have faith or quit paying. Sounds to me like you should be bringing these concerns to your coach and following whatever modifications they make to your plan.
Hey, it's only early February. As you say, a long season. I wouldn't be in any rush to do a lot of intervals and compromise your performance later.