Note: modern Shimano rear deraillers do not have speeds. They all have the same cable-pull, whether "intended" for 6, 7, 8, 9 or 10-speed indexing. But your RD is fine here, it seems.

Part of your issue is that the down-tube of your bike doesn't have a barrel adjuster and isn't designed to accept one. However, I think you could find one that fits into the cable stop that's already on your frame. Ask your LBS for parts like this. Or go to the second link that cascade168 posted - it's the thing you need. You don't need the first thing that he linked, as I assume your frame already has cable stops welded onto the the down tube.

However, this may not solve your problem. Front deraillers, however, have varying cable pull. Now that you have brifters, you probably need to get a road-STI-compatible front derailler. Your Altus FD (my guess, I've not heard of Argus) isn't designed for front indexing with road shifters. This is specifically a problem for triple chainrings.
You can get a Sora FD pretty cheaply. I'd recommend going with the the mickey (barrel adjuster that fits into your existing cable stop) and then buying a Sora triple FD if that doesn't solve things.

I have no experience adapting V-brakes for functionality with regular road brake levers.