Why not doing old fasioned box modeling?Just block out the base shapes and refine further, add some floating details add the barrel and stuff. This part is one of the easier ones, the others are more difficult to be honest.
Best non destructive workflow, is to add a continuous edge (Add Loop) when an object/shape is made up of quads not tri's or ngon's also unsure why you're triangulating in the first place, if I assume this is an initial blockout?!
start with a 8 cylinder, and make your big shapes (primary). subdivide 1-2 (add your secondary shapes). clean up some of the edges, I was lazy to do it properly. Add new supporting edges to the new shape.
@Bek Start with a cube and get the main shape add the curve on the bottom bevel the back and front last add the cuts on the bottom I've been on the computer all day... if this doesn't make much sense, I'll speed modeled it later and upload a vid.