You can't avoid playing with the tongue, especially if you need to split notes. It's also goofy to spend the whole time looking up. Do not attempt blowing out to clear spit; That just makes it worse.
Here's what to do:
If you must do some intense extended blowing, those are times you need to be looking up.
Otherwise, as part of your routine, be aware of when you'll be doing draws, and do them while looking up. When possible work strong draws into your song. Abrupt and strong impulses clear spit better than slow soft draws.
I simply add a strong quick draw arpeggio along the whole harmonica between verses while looking up. There are some blow notes too, but the important part is the stronger rapid draws.
In general, draw stronger than you blow, and look up more when drawing notes. Sure, it affects your style, but so does suddenly not being able to play at all because a reed is clogged.
Harmonicas can be played in a few positions/styles like cross-harp which emphasize different notes. Choose a combo of harmonica key and song which emphasizes the draw notes.
Harmonicas can really force some improv skills, partly because notes are missing and those few which are there are conventionally wrong unless you learn how to work them in, but also because sometimes you suddenly have to work in abrupt draw notes to clear the instrument, and need matching bridge/arpeggio tactics to work those notes back into the piece as well.
Spit can be your friend though. Unless you use some surgical or sex lubricant, you're better off leaving the instrument shell wet if you'll be doing some 40 minute wailing solo, otherwise you'll find the skin peeling off your cracked lips later.