Unfortunately I don’t have any experience with the Cort but I have played the Marcus Miller and they are really well constructed instruments. I was quite impressed especially with the prices.
Now IF you feel comfortable and are within their delivery areas, Thomann Music does sell Jazz necks that MIGHT work for you: www.thomannmusic.com/e-bass_necks.htmlThe issue could be that it looks like your Bacchus is probably a 21 fret vs standard Fender 20 fret but it would have to be measured to be sure that it would fit the pocket AND wouldn’t mess up the intonation.
Buying a new bass could just be faster and easier and it doesn’t look like you could go wrong with either of those. I also wouldn’t ignore Squier’s Contemporary active models or if your willing to go passive the Classic Vibe series. Those are very worthy instruments as well. Good luck with your search!