I think you'll be fine without any additive to oil, but that depends on your oil of course! Too much zinc is bad also, so don't go overboard on breakin oil or additives! I use Brad Penn oil in my flat tappet engines, and I put lots of miles on them. It's the old Kendall factory, and is made to specs for early flat tappet type engines.
I'd want to know the location and positioning of the various components to comment on the fuel draining out. Offhand it sounds like maybe the needle on the floats isn't sealing well, which will let fuel leak into the engine, but also let fuel siphon back to the tank.
I'm still not a fan of adjusting lifters with engines running. It's based more on hearing them click, than really accurate adjustment. I agree with the spinning the pushrod to set lash; as that almost always ends up in things being too tight. Make sure you've got 1/2-3/4 turn after zero with these crummy lifters every cam maker supplies today. The wire clips will pop out if they don't have the extra turn, and then things will get ugly! I've had problems with them, as it took me awhile to understand what was happening to these late style lifter clips.