"Which is it?" I think that the right way is pretty much the way that works for you.
I'm wider than the average bear and like to have my handles spaced well apart. I have maybe a foot-and-a-half to two feet between the ends of my oars, but I use fairly short oars because I used to boat some pretty narrow water. I agree that mashing your fingers or thumbs between the oars is just a little less fun every time you do it. Move your stops inboard, extend your oars outboard, and see how you like it.
Whether the stops are against the horns of your locks, or somewhere inboard is your choice. On most of our local rivers it doesn't make any difference. By the time you're ready to tackle big water you will have developed a knowledge of what works where.
I agree with the comments about losing the Oar-rights. Understand that this is just my own, unreasoning, gut-level prejudice -I despise them. IMESHO, if you have them inserted into your locks while rowing, as 90% of them seem to be, you will never learn the art of rowing, you will just be laboring down the river, hacking and chopping at the water and fighting the up-canyon wind. As for using them to hold your oars vertical in the water when at anchor, well, they'll do that - but what if you don't WANT your oars vertical in the water? I have found that by tweaking the angle of one or both blades, I can slide my boat 2 or 3 or even 4 feet to one side or the other without moving my anchor. I can cover a little more water and fine-tune the angle of the boat.
If you are brand-new to oars and drift boats, try a flatwater excursion or two to get used to how things work. Drifters don't have keels, so moving in a straight line takes some skill acquired through practice, as does jagging a boat right or left to dodge a rock, and ferrying. When you graduate onto moving water, remember the adage, "Keep your ass out of trouble." Generally speaking, you want your stern, your butt, pointed away from hazards. This is because you can pull on the oars using biceps, gut muscles, all your back muscles, and leg muscles too if you have a footbrace. This generates a lot of thrust and acceleration. Conversely, if you try to power out of a situation by pushing on the oars, you're pretty much limited to triceps and upper back - you can't generate nearly the thrust.
Three last thoughts...1. Sliding thru curves and coming out of chutes, remember that an object in motion tends to stay in motion. Your boat builds momentum independent of the current. If the river is thrusting you at a wall or sweeper, don't count on a little curlback to bounce you out of trouble. Begin using your oars to pull away well in advance of contact. 2. DON'T tie a knot in the end of your anchor rope. If you are running fast water or rapids and you accidentally drop anchor and the knot hangs up in the roller you can pull the stern out of a boat, or swamp it. Either way, you have big trouble. 3. Tuck your rod tips inside the gunwales while drifting. It's cheap insurance.
Have fun!