The under $100 bogie changes the game...
My first thought is a TM Heirloom Artisan Horsehide with linen second.
But as I think about living with just one strop, I am inclined to consider the SRD modular paddle. I use a board strop when honing (Kanoyama) because I hone all over the place and a hanging strop isn't convenient, so the paddle might work well if I could have only one. Thank goodness that isn't the case!!