Using a combination of "Support our Party" and "Lower National Unity", I've rendered countries helpless to mobilize until they're actually under attack. By having your party rival theirs in popularity, they get a penalty to National Unity for "fractured government", and then your subsequent efforts to reduce Unity directly have that as a bonus. Once you've reduced their domestic spies a bit, you can set 2 "pips" on "Counterespionage" and 1 "pip" on either "Support our Party" or "Lower National Unity", which is enough to slowly erode their government over time while keeping their own spies from fixing the problem.
In one game, I had FRA down to about 23% NU at the start of hostilities, and had SU down around 55-58% at the start of Barbarossa in the same game. That restricted what laws they could implement before actually being at war, and also meant that I didn't have to trek halfway across Siberia to get the last VPs for Bitter Peace.
Supporting your government in a country that's potentially going to become hostile, and using Influence and Relations (through Trade) to keep them out of a rival faction until their next election, means that they should start to drift in your political direction. Either the rival factions have to spend Influence to keep them from joining you, or else you end up with a lot of allies. A few countries with valuable resources can be turned friendly by the election of officials sympathetic to your cause, and even if they don't join you, you can trade with them for what you can't get elsewhere (a neutral NET is more valuable to GER than having them in the Axis).
Best part is, once you make the initial heavy expenditure (5-10 Leadership points for a month) at the start of '36 to dump 10 spies at once in a couple of countries, and drive out their existing spies before they really get firmly established, it's often fairly "cheap" to maintain that superiority. Playing GER, I had 10 spies making an internal mess of FRA, UK, SU, and US, plus 3-7 in a bunch of smaller countries, and was only pumping about 1.2 Leadership into maintaining ALL of them, with enough spies to spare to place occasional agents in about a dozen others. Compare that to the hefty price of direct Influence (2 Leadership per country), and it's a bargain.