My 2c:

I speak Latvian, russian and a bit of Polish. I could easily imagine a Slavic interlanguage, as knowing russian helped a lot with Polish. Learning russian took a lot of effort, though.

So, besides having a bunch of shared nouns, adding Baltic languages to the mix does not make much sense IMO. Despite having a shared ancestor (in theory), Baltic languages are not very mutually intelligible with Slavic.

Edit:

And also, if it does take on this impossible mission, it should at least be called Balto-Slovio.

Lithuanian native speaker here. Reading the examples in the site I couldn't understand anything, and it sounds nothing like Lithuanian or Latvian. Being able to understand Russian to some extent didn't help either.

I find it hard to imagine such a language, as the languages really are far off from each other.

Proto-Baltic and Proto-Slavic have separated much, much earlier than various Slavic language families. Balto-Slavic is typically dated to somewhere between 3000-1000 BCE. On the other hand, the Common Slavic period is 600-1000 CE (and mutual intelligibility went on even longer). The degree of similarity between the languages is simply not comparable.