Oh it's so exhausting just to get out the door, isn't it? Sigh...
As for the stupid comments from passersby, screw them. They have NO IDEA what they are talking about. The stupid comments happen no matter how you are taking the twins out. People are idiots. I am getting even more offended by these comments now that my girls are getting old enough that they show some signs of understanding some words.
As for navigating stairs, I had this issue with LLL meetings for a while and ALWAYS insisted (and I mean insisted, though very politely and in a very friendly way) on help. I had a couple of moms who helped me. Don't expect moms of singletons to have any idea what you are going through, but don't expect to get around like a mom of a singleton either. Get help.
As for gas, DH got gas for me the first year. I still don't get gas much, and only at full service stations unless another adult helper is in the van with me. This is a job for an assistant if you have one. Or plan a route to a full service station when you have to - I hate doing that but I have my route planned out when I do.
I actually LOVE your sling/umbrella stroller combination idea. But I'm surprised you can't get through doorways with your side by side. The way they are made nowadays they are supposed to get through standard doorways. My side by side navigates really well in almost any situation, even Walmart, aka Store Hell. Is it possible you have an older stroller or even a defective one? Side by sides are made to be very practical these days.
All that being said, there are so many days when I have to almost peel myself off the floor to get ready to go out and then I am so exhausted by the time we get in the car... oh mama I feel your pain. At some point this HAS to get easier, doesn't it?