My favorite board is the NSP Sonic Pro Carbon 14 x 24,25. It's the new version with a squaretail. I ride it on up and downwind, mostly steep short period waves with whitecaps. I have a Carolina too but as it is 25" wide, so I prefer the Sonic even on dead flat water. The Sonic being relatively narrow, yet stable, it feels good to paddle and it is relatively fast even on flat. I know SIC Atlantis fits this category as well, do you know any other boards like this? I have understood that some downwind boards with narrow pintails are tippy unless you have the board so wide (front wide) that they are not comfortable to paddle on flat water anymore? Not actually looking for a board, just asking of curiosity.
Without getting into specific boards, I can share the main characteristic that separates my downwind board from my flat-water board. The downwind board is a newer SIC Bullet 14 which has a planing entry with a fair amount of rocker which is perfect for dropping into and surfing steep bumps off the coast of Maui. The flat-water board has a low and very narrow piercing bow with no rocker so the sharp vertical entry is at water level. Though the boards are the same width with very similar rails, the Bullet is slow and hard to push through the water due to the flat-bottom/rockered entry but the board comes alive and takes off like a rocket when surfing good-sized bumps. or small ground swells. The flat-water board feels frictionless on flat water and glides fast and beautifully with each stroke, pure joy on flat water. It is fun to down-breeze on lakes with small whitecaps but that low sharp bow would be a big problem in decent sized ocean bumps or surf. Though I love both boards, the very different nose entries mean that neither one could be considered a combo downwind and flat-water board. On these boards, the nose entry has much more effect on speed and efficiency in different conditions than overall width or other factors (related to your question, both boards have identical square tails).
I hope that gives your curiosity something to play with.
I can recommend at least for the 170 lbs range the Sunova Torpedo 25.5 and Naish Maliko 26. Both are great downwinding and pretty fast on "flat" and great in chop. Zero issue with tipiness.
Not many people have one but a JL Sidewinder I find good for DW and flat water long distance paddling AND it's the best looking board.
I have a JL M14..i take it trips along the coastline and surf weak swells on it too. Picks up small swells great.