If it was me, I'd go get the TC-14E II and stick with the D800E. The sensor is better in all round IQ. You can use it in 1.5 or 1.2 (4x5) crop mode if desired. The D5300 has a high ISO of about 1300 and the D800E is nearly 2800 per DxO specs. So the hi ISO sensor noise is a good bit less in the D800E, helpful in getting shutter speeds up where they need to be even using slower lenses, and in the case of that the 300 afs F4 that is not a VR lens if I am not mistaken, or for more depth of field. The D800E view finder is larger by around 80% and brighter, and works faster and better in low light conditions, plus 51 focus points as opposed to 39 plus a larger number of AE modes and areas. The shutter delay is about three times longer for the D5300. The D800E has an on board drive motor for non-motor AF lenses, allowing the option of there use if available, the D5300 doesn't. D800E has two memory card slots and the very Fastest write CF cards can be a useful feature if you get in a situation where you bang off a bunch of frames, faster recovery, plus I would guess the buffer memory is larger in the D800E as opposed to the D5300. Battery life is a good bit better in the D800E and far superior if you have/use the MB-D12 battery pack, I've shot over 1600 frames and not even got close to running out of juice. Seems 600 frames is the number that the D5300 will do on a single battery.
About the only thing that is better for the D5300 is that it is lighter, and if you are really concerned about IQ then I'd be shooting on a gimbal headed tripod or a monopod at least and then camera weight is much less of a consideration.
Later Larry