Go to your amp and select the "low-mid" control in your EQ. Anywhere between 250Hz (where I normally set mine) and 550Hz will work. Now boost it to about 1:30 and give it a try.
The reason that "mid-scoop" sounds OK by yourself is that you are not playing at gig level and the mids are easier than the bass or treble to hear at lower levels. To get that same sound at higher levels, especially when playing with a group, you need to boost the low-mids a bit. If you boost them too much, your sound will honk at you. If that happens just slowly dial the boost down until the honk disappears. I use a passive Jazz with all my controls on the bass dimed and typically run my Eden or DNA amps flat with the exception of some small boost in the low mids.
If I have semi-parametric controls, I'll boost the low mids up to about 1:30 right around 250Hz because I like the sound I get. I'll do that with my Big, class AB, Eden WT500/800, and also my class D, Eden TN-226 amp. If I'm using my DNA-800 amp or my WTDI which is a DI stompbox with a built-in Eden WT preamp, I'll boost it at 500Hz because that's the only low mid frequency available to me with those two. If I am recording at a pro studio, I will put that slight boost of the low-mids at 500Hz because my bass records freaking great on the raw takes like that.
Before you start swapping out electronics, try adding a little boost in the low-mids. Those low-mids are what gives the bass presence and definition in the mix. The bass drum owns the lows, the guitars and keys eat up the high-mids and highs and the bass owns the low-mids...so use them! Also, just as FYI, adding distortion to your bass makes it much harder to hear you in the mix. So try it without the overdrive or distortion with just the low-mids boosted and after you get a good listen to that, go ahead and add the distortion. I think you'll see that you are much easier to hear in the mix with a clear sound and a little boost in the low-mids.
Below is a clip from a few years ago where I'm playing with the J Badders Band at Evelyn's Tavern near Clear Lake. We're playing "Somebody to Love" by the Jefferson Airplane, which has a fairly active bass part. I'm playing my '82 Jazz through an Eden WT500/800 into two 4Ω Eden EX-112 compact cabs. This amp is a dual powerblock amp, so I have one cab plugged into each power channel of my amp. I strive for a clean, clear, and articulate sound and this rig delivered it nicely for me for a couple of years before I got my DNA Endorsement.
You'll see that the bass is well defined and easily heard without the need to raise the level up so high it buries the rest of our 5-pc band. The recording was from a friend's iPhone, so it's not a great recording but you can easily hear every note I'm playing throughout this song. The only boost was 250Hz in the low mids up to 1:30 on the boost/cut dial. Everything else is set flat, the compressor is bypassed and the Enhance control (Shape) is turned to the off position. Unfortunately the vocalist, Joan, is on the other side of the stage and you might get a glimpse of her every now and then between myself and our lead guitarist. This was just the second time we'd performed it. But that is what a slight boost in the low-mids can do for you.