I'll just throw this out here in regards to not doing CF programming and still being good at CF....
There was an OCS candidate I met, who was previously enlisted, and he served with Force Recon. In talking about training, he said that he pretty much just lifted heavy and ran. Then, like the naive idiot I am, I said to him, "oh you should try Crossfit, it'll blow your workouts away." He, being a kind and mature Marine, took me up on my advice, I think just to humor me. He went to the local CF affiliate, and they gave him Fran his first night.
Anyways, I'll cut to the chase. He did Fran in under 2 minutes. Everyone remarked to him how they wished they had brought a camera, asked him to come back and do it again, and apparently he got so much attention for it that he actually did not want to return. When I caught up with him, he remarked at how easy the 95 pound thruster was and asked me how does anyone get stronger using such light weight. My stupid answer, "you just go faster."
Just to give you an idea of his fitness level, I'll also make the point to mention that he could do reps with a 225 military press, and when we ran our PST, he ran the 3 miles in under 15 minutes, crossed the finish line not even out of breath and immediately lit a cigarette.
The point I'm trying to make is that obviously he had more than adequate strength from his weight lifting (not weightlifting) and PT with the Marines, and his cardio/endurance base was more than adequate as well likely due to running hard with a pack on uneven terrain among other things like O-courses and room clears, etc. So, you're getting solid advice here. You CAN improve your fitness level by working the parts separately.
I, like you, thought that I was going to improve my fitness level by stacking WODs and adding strength sessions, so I was basically working out 2-3x a day. Strength workouts early, and metcons at night. Now that I've stopped that... my strength has shot through the roof. Take the advice you're getting here seriously. Less work, more recovery = more progress.