Partitioning Digits into Distinct Integers
Jelly, 14 bytes

ŒṖḌD$ƑƇḌQƑƇLÞṪ


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A monadic link taking a list of base-10 digits and returning a list of integers. 

Added a byte (and switched to numbers) because of the zero padding issue. 

Added 5 bytes to fix a further issue with zeros pointed out by @KevinCruijssen - thanks!

Explanation

ŒṖ             | Partitions of list
  ḌD$ƑƇ        | Keep only those invariant when converted to integers and back to lists of digits
       Ḍ       | Convert from lists of lists of lists of decimal digits to lists of lists of integers
        QƑƇ    | Keep only those invariant when uniquified
           LÞ  | Sort by ascending length
             Ṫ | Tail