Laces Slipping on Koflach boots

I was ice climbing with my new to me used Koflach Plastic Boots. They are the older orange ones with open cell foam inserts.

I noticed that after a few pitches that the laces were loosening and I could feel the lack of rigid support around my lower leg and ankle.

Has anyone replaced their laces and what do they replace them with?

I have used paracord in the past on basic merrell hiking boots and it wasn't too good.

I also noticed that the open cell foam inserts didn't keep my feet warm around 0°F. Any cheap or used closed foam insoles available?

Thanks.