I have a FX lens that I use!
I like to buy used, so preferably under $400 for a used Camera body.
It must be a newer FX lens with AF-S if it auto-focuses on the D5300. The D3000/D5000 series require a lens with the focus motor in them (AF-S) to auto-focus, where the D7000 series have camera based auto-focusing for those older FX AF lens that use a screw drive to auto-focus rather than the lens based internal motor. The D7000 series works with both focusing systems. Not certain, but also believe the 3000/5000 series had issues/limitations with off camera flash triggering and HDR was manual single shot adjustment if either of those are important to you.
$400 budget used. While tight to meet, a couple of issues. As you state have a photography business, if in the US, any equipment purchase is tax deductible against profits, and how many shoots would it take to make up the difference when exceeding $400? Assuming keeping the D200 as a second body, but if selling don't know if those projected proceeds are included in the $400 budget. With new bodies typically on sale, and used not, the price spread shrinks to perhaps one photoshoot. Looked at B&H for general reference pricing (didn't check KEH or Adorama), and while full frame is tempting, would recommend the D7000 series if you don't need full frame. Actually, at times I wish I had a crop sensor with wildlife and sports photography.
FULL FRAME: (lower numbers are older models)
D610 - ($1497 new), $599 (grade 8), $689 (grade 8+), $759 (grade 9)
D750 - ($1297 new on sale), $972 (grade 9), $907 (grade 8+)
Avoid the D600 (and SB900 flash) as had issues resolved by Nikon issuing the D610 rather than firmware resolution. Did the same with the overheating/shutdown SB900 flash, issuing the SB910 rather than firmware resolution of the problem. The D610 was actually my last Nikon and was looking at upgrading to the D750 vs jumping to Sony.
CROP SENSOR: (lower numbers are older models)
D7500 ($796 on sale new, $749 refurb), none used
D7200 (unavailable new) $565 (grade 9) $612 (grade 10)
D7100 ($696 new) $399 (grade 8), $439 (grade 9) $469 (grade 9+) $499 (grade 10)
D7000 (no longer sold new) $299 (grade 8), $339 (grade 8+), $369 (grade 9), $389 (grade 9+)
The D7000 was my last before upgrading to the D610
That's a start. Each site (B&H, KEH and Adorama) will define what their condition grading scales are and any warranty they issue on used. Also DP review will have a review of each of the cameras in their database, and as part of the review will reference difference from model replacing. That may help you when trying to decide between models in the same series