Alas, the Sicilian is not an opening for the faint of heart. It strives to exploit the complexity and dynamic nature of the position, so it is quite hard to find shallow solutions. At risk of avoiding your question, I would say that it is best, if you want to avoid theory, to pick up a line more alike the open game. Still, I did my best to show a nice plan.
First, lets handle the move 2 anti-Sicilians (2. c3). In general, they are in fact designed to reduce complexity, so a small bit of knowledge can go a long way. Against 2. Nc3, you should continue with the move that you use against 2. Nf3. The closed Sicilian is a relatively complex opening still, but I find that up until 2000 USCF (or 1800 FIDE), Closed Sicilian players do not have a grasp of theory, so you can likely be safe to skim on that section of your study.
Against the Alapin Sicilian, the general recommendation is 2... Nf6. However, I think the line 2... e6 is underrated, so you may be able to use it to avoid theory. After all, particulars have to be studied individually. It is recommendable to find a personal line that is intuitive, but your general idea is to play d5.
For a generic solution against the open Sicilian 2. Nf3, you will want to avoid playing the Najdorf at least as every chess player and there grandmother has a way to play against it. Your try of using a Dragon-esque system was likely difficult as it is a highly theoretical variation and even then, semi-dubious. In addition, it seems troubling to play any line starting with 2... Nc6 due to the Rossolimo and the very sharp nature of the lines here.
My recommendation has to be the Kann variation (2... e6 3. d4 cxd4 4. Nxd4 a6). While it can be a bit difficult to learn, it is one of the less sharp lines and it is seldom studied by lower rated players. I would try playing around in some relatively short games and seeing where you falter. There is plenty of material on the specifics of the Kann variation, but the general idea is to play Nf6, d6, Be7, O-O, Nbd7, and Re8. This sort of "hedgehog" style position gives plenty of opportunity to both sides and should not require too much theoretical knowledge.
Good luck :)