What is the best way to get temporary smartphone data service across multiple countries?

My specific question is about Europe: I'm going to be going through Germany, Czech Republic, Austria, Slovenia, Croatia, and possibly Bosnia/Herzegovina and/or Montenegro. (I live in the USA.) However, I'm interested in the overall question for travel in general as well. Basically what I want to know is what is the overall least painful way to get access to a mobile data network while travelling among several countries.

I have seen previous questions here, here and here. The main three options described there are:

1. Use an international roaming option from your own home-country cell company.
2. Use an international SIM card such as keepgo or the like.
3. Buy a local SIM card in every individual country you travel to.

Option #1 is not available for me as I use TMobile prepaid which doesn't offer international data roaming. Three years ago I went to several countries in western Europe and basically used option 3, but there I was just using voice/text because I didn't have a smartphone at that time. It worked, but it was a bit of a hassle, not least because it was difficult to get clear information about what will happen when you buy a SIM card in one country and use it in another country. For this trip data is more important to me than voice/text (I could probably forgo voice/text entirely), but the multi-country issue is still the big question mark.

What I'm wondering, beyond what is covered in the other questions, is essentially which of solution #2 and #3 is overall more practical. Specifically:

1. Is it always the case that every single national border crossing means you need a new SIM card to avoid impractically high fees? Most of the questions I've seen about this are from before the recent EU regulations on roaming charges. I'm not an expert on those regulations, but from what I can find they seem to have somewhat lessened the pain of multi-country travel. Are there are rules of thumb as far as roaming rates (e.g., if you go from one country to a neighboring country, will the rate increase typically be less than if you go to a more distant country)?
2. At what point does the hassle of buying, installing, and adding money to multiple SIM cards (with the language-barrier problems likely to be present at each step) outweigh the drop in cost? Also, there can be money wastage associated with getting a new card without using everything on the old card. On some of the country-specific provider sites I looked at, it's not clear what will happen if you take one of these prepaid data SIMs outside the country. Will they just not work, or will rates just skyrocket?
3. How does performance compare between the local providers and a package deal like keepgo?

Basically I'm looking for practical guidance on where the happy medium is between keepgo's simple "$8/day 50MB" and the opposite extreme "maybe you can get cheaper rates by buying 5 different SIM cards and loading them with just the right amount of money".