You have my sympathy. I am hard to fit too, so when I find something I like, I get it and worry about building an outfit around it later.
When I buy something new, I do an outfit try-on session at home. If I can't find anything that works with the item, I try to figure out why. Is it the color? The fabric? The length? The neckline? Or maybe I need certain styling hacks to wear the piece well (tucking, cuffing, etc.). Then I can start to form a shopping list of pieces that will help me wear the orphans.
Sometimes I also look online for outfits that incorporate a similar item to the orphan so that I can get ideas of how to complete the outfit. For instance, if I have an asymmetric midi skirt that I'm having a hard time with, I might search for "how to wear asymmetric midi skirt."
I have found that the orphan situation improved for me over time as I added items to my wardrobe that were in a variety of cuts and silhouettes. This means I have a pretty good chance of having something on hand that can complete an outfit. I now have only a handful of orphans. I do have a fair amount of pieces that aren't mix-and-match, however, and have to be worn with a particular top or bottom to look good. I don't mind because I like repeating outfits.
ETA: I have tried the solution of not buying a particular item unless I can also buy completer pieces at the same time, and that's simply impossible for me. Since my size is not very plentiful at retail, I have to buy the item in isolation and worry about completing the outfit later. I usually shop online for the completer pieces. If I don't have much luck, I may decide to return the item unless I'm in absolute love with it.