Even with a tune, the injectors are going to be too big. You can't dial them back enough. Fuel flow is controlled by the length of time they're held open. Well at idle those times get very low. Once they get to 1ms, they become unpredictable and the ecu can't control them.
The only thing you can do is get some stock injectors. ebay or junkyard.
If you keep running your engine rich you'll wear out the bores and piston rings. Excess fuel washes the oil away.
How to get more air into the motor? Well that's the trick isn't it. More air = more power. That's the whole point. Turbo or serious N/A build... but even so, that doesn't increase air into your motor at idle. So for setups that need to idle and require ridiculously large injectors, you can do what Edelbrock does and have two separate sets of injectors on the same intake manifold. Or you can turn the fuel pressure way down at idle and find a way to ramp it up more aggressively than the stock vacuum setup.