Firstly, let me apologize if this has been asked ad nauseum. I did search prior to posting. Being new, I don't know if I missed something. Also, I must admit that I am a guitarist and pianist who started playing bass out of necessity, so my terminology might be a little off.
Now, my question:
For recording purposes, I have been using a MIM Fender Jazz Bass, with DiMarzio UltraJazz pickups, mostly into a DI. However, the stuff I record is pretty diverse, so while the J sounds great in some mixes, it is lacking in others. In the fall, I rerecorded a troublesome bass track using a P/J, mostly with the P pup. In my opinion, it was perfect for the track. It had a certain presence, and grit that cut through the layers of distorted guitar on the track, without being too nasal. As such, I have decided to look into getting a P, or P/J bass. The problem is, I have had some issues with Fender stuff in the past, including neck pocket slop, and electronics gremlins. Even now, the J Bass has probably the most finicky neck I have ever experienced. My non-Fender guitars have been extremely stable, by comparison. Maybe it is the due to the flatsawn neck, as opposed to the quartersawn in my guitars.
Considering my reservation, what else might I look at to get that P sound, with a max budget of $1500? So far, others have suggested looking into a G&L SB-2, Carvin PB4, or possibly a used Lakland, or Korean-era Skyline.
Aesthetically, I am not really looking for anything fancy. I am mostly concerned with sound, playability, and quality construction. Also, having played on a Ric 4003, nothing with hard edges. That thing dug into my wrist like no other.
Anyhow, sorry again if this is a redundant question. Thanks for any suggestions.
ETA - if anyone has any suggestions for dealers to look at in the Cleveland, OH area, let me know. A lot of the old ones have closed shop.

Now, my question:
For recording purposes, I have been using a MIM Fender Jazz Bass, with DiMarzio UltraJazz pickups, mostly into a DI. However, the stuff I record is pretty diverse, so while the J sounds great in some mixes, it is lacking in others. In the fall, I rerecorded a troublesome bass track using a P/J, mostly with the P pup. In my opinion, it was perfect for the track. It had a certain presence, and grit that cut through the layers of distorted guitar on the track, without being too nasal. As such, I have decided to look into getting a P, or P/J bass. The problem is, I have had some issues with Fender stuff in the past, including neck pocket slop, and electronics gremlins. Even now, the J Bass has probably the most finicky neck I have ever experienced. My non-Fender guitars have been extremely stable, by comparison. Maybe it is the due to the flatsawn neck, as opposed to the quartersawn in my guitars.
Considering my reservation, what else might I look at to get that P sound, with a max budget of $1500? So far, others have suggested looking into a G&L SB-2, Carvin PB4, or possibly a used Lakland, or Korean-era Skyline.
Aesthetically, I am not really looking for anything fancy. I am mostly concerned with sound, playability, and quality construction. Also, having played on a Ric 4003, nothing with hard edges. That thing dug into my wrist like no other.
Anyhow, sorry again if this is a redundant question. Thanks for any suggestions.
ETA - if anyone has any suggestions for dealers to look at in the Cleveland, OH area, let me know. A lot of the old ones have closed shop.