The problem you're having comes from the octave equivalence of the software. In other words, it expects you to give it the frequencies 1: in ascending order and 2: limited to one octave (by default, although other periods could be used).
In order to fit your desired notes into that description: Decide which octave you want to start from (I suggest the middle one, starting with C3), then take the notes outside that octave and double or halve their frequencies as necessary to fit them between one C and the next C.
You also have two different Ab's. That's trickier, but since there's no A in your scale I suggest simply mapping the slightly higher one to A.
It might sound more complicated than it is, it's pretty quick work. I tried it from curiosity, and the frequency list ends up being:
C3 = 264 (assign this one to the Diapason for convenience)
Db3 = 285
D3 = None (click the scale degree number and choose unassigned)
Eb3 = 319.5
E3 = None
F= 348
G = 396
Ab = 417
A = 426 (this is your second Ab, octave reduced and mapped to the A key)
Bb = 528
B = None
C4 = the pattern will automatically repeat upwards from here, giving access to the fourth octave notes you listed, and also downwards from C3 giving you the second octave notes you listed.
I played around with it a little. It has some just 3/2 fifths in it, making me first think this might be a just scale of some sort. Pianoteq identifies the ratio of C3 to A4 as 71/44 (!!!) a ratio I've never seen anywhere in tunings before. Because 71 is prime, and I've never heard of anyone working in prime-limit tunings above 15 to any real extent, I doubt you got this scale from just intonation nerds like myself. Where did you find this exactly? "All over the internet" is not very specific.