I get the same jammed-up accidentals, even with just one measure on the line. There are programs that will handle this, but you may not like that default spacing either.

Adrian, this is not perfect, but it looks decent. What did you do. Did you manually move every note? Also, if you doo that, is it possible to lock the measure spacing, so it won't change?

Thanks, Igor

I used another program. If I had to do it in Finale, I would probably use a key signature to avoid all the accidentals, and I generally avoid key signatures in the music I write.

Adrian, I am dealing here with atonal music, so key signatures are irrelevant. I wanted to let you know that I found the cause of the problem. My music spacing option from the document preferences somehow changed from default. It is easier than I thought.

Thanks for your help! 

If your program changed from default spacing, then mine did too; because when I typed in the notes in your example in Finale, I got the same jammed up tuplet that you did.

Glad you found a solution.

This is how I did it. Document options - Music spacing - Spacing Width. "Use spacing width table" instead of "use this values". Apply changes. Click on the measure in question while in speedy entry. 

Thank you for providing your solution.

If the part is played rapidly, maybe write it as an arpeggiated chord, or two arpeggiated chords (wavy vertical line in Articulations Tool, which can be customized, say, bottom note at -512 to 0 top note. Just a thought.