I have the UJ2 for my DK40se. If I were you (and committed

to getting a 4n1), I'd get the HJ2. The UJ2 is considerably heavier as I recall and is really designed for bigger loaders. Your loader is rated by Kioti at the pivot pins but WRLong rates their 4n1s by mid bucket lift and I think the KL130 would come in at less than 1000lbs mid bucket lift. I believe (haven't checked) that puts you right into the HJ2 range.
The CK30 is a heavy tractor and I would be concerned about the HJ2 in dozer mode as it is possible to bend that lower edge by hitting a submerged rock or stump. That is a disaster for a 4n1 as it won't close properly after such an injury.
You may have seen some of my posts about my experience with the 4n1. I am lukewarm about these implements especially for people who already own a standard bucket and a
grapple. There is almost nothing the 4n1 does that is not done better by the other two implements. If you spend half or less of what a 4n1 would cost and get a box blade then there is nothing at all the 4n1 really adds except the Swiss Army knife factor.
I do like using the 4n1 when I am using a BH to dig out stumps because the 4n1 can lift out a single stump with no trouble and can then be used to clean up the hole very nicely. However, you could do the same with a regular bucket and a chain or with the
grapple and a shovel. Hard for me to justify the near $2K price for a new shipped 4n1 frankly. I got mine used off ebay for dirt cheap so I'm happy with it but I'd be disappointed if I'd spent that much (considering I already have standard bucket,
grapple and box blade).