Everything stretches, get proper role thick as can go through your pulleys.
Not dyneema.....the only stretch you get with dyneema is what is engineered into the cord.
You can buy quality dyneema cord at any rock climbing shop. It is what is used for slings. Ask them for '3mm accessory cord'. The strength of dyneema cord for a given diameter is crazy. I've taken some big falls onto thin slings...
I remember a friend of mine who has a farm trying to break some old dyneema slings with their biggest tractor....now that was a fun day
Or go to a specialist fishing shop and get some 49 strand wire trace (sharks etc) and some 'double crimps'.
Paracord comes in various different types go to the Bushcraft store to see the differences.