In the end the solution might be to get a Ti sidewinder cone, designed to fit inside the pot, and a pot to match. I think the smallest might be for the 0.6L Evernew Ti pot. This is a bit small if you plan to cook typical dehydrated meals in the pot. With the 0.9L version of the pot you can get the cone inside, with the added perk that the 12-10 stove will fit inside as well - just barely. Plus a spork and lighter.
Just looked and unfortunately doesn't look like they have a sidewinder for the MSR Titan 0.85 (they do for the 1.0 though!), but the pot may be cheaper than the cone. Maybe you should consider a different pot if you really care about this. The ones that work with the sidewinder are the ones that are wider and shorter - less mug-like and more pan-like.
I had the same problem, I had a 0.7L Snow Peak pot I really liked and have been using for years, but it was another one that was too narrow. There was just no way to put it all together, with the case and all, that wasn't huge and awkward and multi-component in terms of the packing, at least from my point of view.
Here are some pictures of what I ended up with as my ideal compromise, if it gives you any good ideas: