Not sure what the issue is here. Is it a lack of proper tooling to drill and rivet, or just a lack of experience in these skills? I would say that your best bet, if you don't want to rivet, is to do a screw build and weld it as per the tutorial here. That way you would be compliant, without doing so much welding that you might warp something. You will still have to drill holes, and you will also have to tap them, but that can be done by hand with simple tooling. I am not recommending that, but it is a better way to go than trying to weld the whole beast together.
As to the large trunnion rivets, you can screw it together there too. But you will need to be creative. One way is to have a custom set up made, consisting of a taper head 11/32 rivet that is fitted to the 60 degree chamfer on the side plate, long enough to reach into the opposing side plate. Basically you are making a big, long nut. It would then be drilled and tapped to fit a button head screw that is also turned to fit the side plate chamfer. It then acts against the side plate chamfers like a rivet when tighened, squeezing the assembly together. The upper trunnion, right side rivet/nut needs to be flat headed to clear the cover pivot plate, but the lower can have a dome if you want. But remember a screw build must have the deep penetrating welds at the top plate, bottom plate and trunnion.