I'll second the Zoom F6 recommendation. I moved from DR-680 to Zoom F8 and have been quite happy with it. I've not used the F6 but its essentially a more compact F8 with a few less channels. Same overall format. I don't consider 32bit float recording a necessary or significant upgrade for an experienced taper but others will feel differently.
It's unfortunate the DR-680 is being discontinued, as it was pretty much unbeatable on both a cost per channel and ease of use basis IMO.. and a few other things like having digital in/out. Not sure on the business side of Tascam these days, but I wonder if we will see a replacement for it at some point.
Lots of love for the SD Mixpre 6 here at TS too. I've not used one, but in comparison with the DR-680 it strikes to me as significantly more complex with regards to setup, operation, and potential pitfalls. Most get familiar with it easily enough I suppose, but the only multichannel recorder I found more easy and straightforward to use than the DR-680 was the R-44. Might keep an eye on the yardsale for one of those (Oade OCM version preferably) if you'll only need 4 channels. They are hard to beat for what they do, simply. You won't get such modern conveniences like monitoring on a phone though.