I hunt really thick stuff myself, my Topper with a 28" barrel has the same overall length as your 870 cut to 23.75" so we are both in fact using the same length gun. Like you I don't care for really long shotguns either but break action guns such as a Topper are very compact so you can get away with a longer barrel compared to a pump.
An 870 with a 20" barrel has the same overall length as a Topper with a 24" barrel which was one of the op's choices and what I recommended for a dedicated turkey gun.