Actually, with cheap libraries and unis, getting all the buildings in place to research shouldn't be that painful. Heck, a university costs us just as much as a market. I'd be wary of pumping all our cash into the AI to catch up. We're not that far behind....feeding them lots of gpt can actually increase our problems, unless of course a 2fer is available. In one of the LK games we explored this and found that self research on Deity is a pretty good deal if you have a decent area to work with.
I think the only real way that silent speeds things up is the lack of diplomacy. You can just burn through your turns worrying only about the empire and keeping it optimized, rather than juggling deals around.
As for the nukes...well, the only way I know of to prevent it from happening is to prevent them from having the resources they need. If they have them and you hurt them enough, they'll fire them off. Its really only a large nuisance unless they manage to wipe out your entire workforce. If we do just research to Panzers and go ballistic, we may be able to avoid them, but I wouldn't count on it. They have a way of showing up when you least want them to.