It's difficult to advise without seeing the child in the seat, but I can try to give some general advice. You could also go back to your retailer for support or send an email to Kinderkraft.
With a lot of these all-stage car seats, the infant insert is intended to be used for the entire period where you'd normally have them in an infant carrier, and generally if the straps are too loose to be snug on the child's body without the insert, that usually means you need the insert back in.
I have had a look at the instructions and they aren't hugely clear, but they do advise to use the insert until 76cm, which could be interpreted as until minimum 76cm, or until the child would be considered large enough to sit in the (old style) "Group 1" stage, which is a bit more subjective. With this type of insert, it's common for the head piece to detach so that older babies can still have the body support without the extra head support that they don't need any more, but the instructions don't really say anything about this.
Straps definitely need to be snug, as the purpose of the straps is to reduce and stop any movement of the child in a car accident. Loose straps will prevent this from being as effective, which means higher risk of injury, or worst case scenario potential ejection from the seat.
Have you checked if the headrest is in the right position when using without the insert, and whether a lower headrest position helps with tightening the straps?
Also that the straps are not getting caught up in a part of the mechanism anywhere?
With the insert in, where she is sitting on the buckle, I would try raising up the headrest a bit higher, and then kind of sitting her higher up in the seat and see if that helps. You do this by sitting her in the seat and then place your forearms either side of her body and sort of "scoot" her up the seat.
It is also easier to fasten the straps when they are made very loose - so get her positioned comfortably, then find the buckle strap, find the two buckle tongues, check they aren't twisted, lock them together and insert into the buckle. Then you can pull the slack through the buckles, upwards, while pulling the tightening strap with the other hand, this should make it easier even when they are sort of sitting on the buckle.
This is not the same seat but a general video if you prefer visuals:
Do you know how tall your LO is?
Also you might want to know, although the forward facing position is allowed from 15 months onwards, it is much safer to keep children rear facing as long as possible. This seat allows rear facing up to 105cm so it would be recommended to keep her rear facing, ideally for the whole 105cm, but certainly for now - I would say 2 years is a better minimum to aim for than 15 months.