Nice looking FEL Hooks and Sling! Most hardware stores have rings that you could use or just buy a shackle. That strap in the picture could probably lift your tractor (not legally) with a 30 degree lift angle without breaking. Just don't let anyone under the load!!!
Regarding your sling in the picture I have lifted many thousands of loads commercially with Synthetic Slings and have never broken a sling or accidentally dropped a load. If that sling has a rating of 4k lbs then the actual breaking point of the sling is many times the rated capability. All the slings that I've worked with had a 5 to 1 safety factor. OSHA Standards 1910.184 & ASME 30.9 were the final word regarding slings used during commercial lifts but they left everything up to the FAA unless there was an accident.
FYI: There is a loss of lift capability formula for OSHA Approved Synthetic Slings that are used at an angle of less than vertical. Just eyeballing the sling in the picture I would guesstimate a sling lift angle of approximately 35 degrees which would reduce the 4,000 rated sling to a safe "legal" lift of 2,296 lbs. I'd probably derate it to a 30 degree lift angle and allow a 2,000 lb load. I always kept a Sling Angle Chart with my lift helicopters and with my lift ground crews for drop in visits from the FAA especially when lifting in densely populated areas such as going vertical 500' between the high rise buildings of San Francisco and other West Coast Cities. I normally used a 125' to 150' Wire Rope (Cable) connecting the helicopter's main hook to the Synthetic Lift Slings holding the load. Now if I was lifting out in the country without the FAA (Fanatics Against Aviation) prying eyes I'd use common sense.
I personally would use a Synthetic Sling connected to your load instead of a chain to prevent damage to the load but for personal use you use what you have. I use short lengths of braided nylon fire hose around the slings to protect the sling from sharp edges.
Jim