I actually have access to a reflow oven. Would you guys recommend learning how to use that?
As you have discovered, applying paste is not automatic. Even with a stencil, getting good results is not automatic. There's a 20 page thread on manual solder paste dispensers in the "other equipment" forum, and mike58's dispenser looks pretty darn good. I try to avoid leadless parts, but if I have to do any on a large scale, I will be giving one a whirl.
For any SMD with exposed leads, meh. I took a long walk down that path and even bought my own reflow oven. The oven works fine. But it's in storage. Unless I need to do a lot of leadless parts, it wastes my time.
For high pin count leaded packages (TSSOP, SSOP, SOIC, QFP, etc.) I find it easiest to just load it up with solder, making sure every joint has been soldered but completely ignoring bridges, then going back with wick to clean up the excess. It's very fast and the result is clean and consistent.
You can drag solder with any tip, but I swear you can do it just like this. And then clean up the results with the iron, no wick. If you use a large CF tip. Simply like magic. Once you get the hang of the tip, you can progress to tilting it to adjust for the amount of solder and not even make the bridges to begin with. It's impossible to describe the difference between it and all other tips and to do it justice.
For example one tip I think I've seen is to extend the last pin on each row to act as a reservoir for excess solder.
You would not even necessarily want to do this with a CF tip, because that would just be extra wasted solder, and you would need to pick up solder more frequently. I can often solder all the QFP/SSOP IC's on a board without stopping, just picking up a little solder from the decoupling caps.
With a CF tip, solder is your bitch, and you control it like a puppet on a string.