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Personally, I tend to take Influence first just so I can do cheap annexations/integrations as soon as possible. But as Bri says it doesn't make too much difference here. Particularly with PUs like the ones you mentioned, which you don't really need to be in a hurry to integrate.
So some rather big vassals to inherit by RNG.
Shifting my collection point to the Venice node while conquering all of it means that the trade from the Balkans, Anatolia, Syria, Egypt, and so on can be routed there. It's my standard Austrian strat.
Blob out and stack diplo rep. I just inherited a full-sized Burgundy this way as Venice (got the Burgundian Inheritance, and fought Austria to keep the Lowlands so it was a very big Burgundy, but never got the Duchess of Burgundy Dies event). Had enough diplo rep and development to get me like 26% inheritance chance.
Let's note areas the two sets are equal: both give +1 diplo relations, and both give +2 diplo rep.
For the first, you need to establish and upkeep good relations with either 4 electors, or, if you're an elector, 3 electors, and that ensures there's exactly no possibility you won't be re-elected. That's a task much easier to do if you have additional Diplomats. You'll get a third additional diplomat from a policy if Admin is your second idea group, or, if you're intending not to stay Catholic and so you select Religious as your second idea group, you get a policy that will help with the process of the transition to the new religion when the time comes. And for the second issue, you get an Improved Relations buff, and your total Improved Relations affects decay rates for diplomatic relations adjustments (making the decay rate slower for positive adjustments, and faster for negative ones like AE). In other words, that Improved Relations buff will make your AE go away sooner.
By comparison, Influence doesn't have any of that. Influence is focused on keeping your subjects loyal, improving the benefits the subjects provide to you, and making it faster and easier to integrate them. Here's the thing: for the most part, those benefits are meaningless for a PU, which you have a lot of. PUs don't provide income to you, so the improved income from the idea set doesn't get you anything. Unlike most other subject types, PUs also compare only their own strength (military and economic) to yours, rather than the sum of the strength of all subjects compared to yours (as a regular vassal does). So liberty desire from development is going to be much lower, and their overall liberty desire is also going to be much lower, too. And, you can Support Loyalists with a PU for +20 loyalty, which you can't do with regular vassals. Lastly, if your diplo rep is high, you can instantly integrate a PU (it's random, though) upon a new ruler taking the throne in your country, so you mostly don't want to diplomatically integrate them anyway (meaning that the cost reduction to that is pretty moot for a PU). But even if you did want to, you can't for 50 years anyway, and guess what you'll have at about that time... a third idea group, which you could use to select Influence if you picked Diplo as your first idea group. Perfect timing for when you'd even be able to integrate them anyway.
That said, it's also worth noting that you get a stacking relations penalty if you integrate an HRE vassal, so I'd make the case that selecting Influence even as your 3rd idea group in HRE play isn't necessarily a good choice. Remember that as a part of centralizing the HRE you will get all HRE members as vassals anyway, and integrate them for free in the end, so your objective should be to be releasing countries out of HRE neighbors and then forcing those countries to join the HRE (if they don't do it on their own), not acquiring vassals (because they'll become your vassals later anyway). I like Diplo, Admin, Religious, then Influence, personally. You'd pick up Religious in that case right as the reformation is occurring, making it easier to counter the effects of reformation if you plan to stay Catholic, or easier to transition if you switch. Admin as your second choice is a solid pick for your second idea set all around, and gives the policy for the additional diplomat. Between that and the other added diplomats you'll have from Diplo Ideas, government rank, reforms, etc, you can easily keep all the HRE members at topped off +90-100 improved relations, which gives you a lot of room to accumulate AE without anybody even thinking of a coalition.
It is absolutely viable with Bohemia as well, particularly if you reduced their size by seizing either Prague (for the Great Project giving more Imperial Authority) or Cheb (for the juicy gold mine income) - in fact, before they added decisions allowing you to steal it, this was the only way (and probably still the most efficient way) to become an HRE Elector yourself to further secure your own Emperorship permanently.
Influence is great with a smaller country when you want vassals but the liberty desire is a problem. And you want vassals to get the noble privilege that gives +2 diplomatic relations to grow powerful quickly through vassals and allies.