There is plenty you can do with a lighter tire. On smaller tractor tires try to get them airborne and to flip. I got plenty of work a few years back while coaching football players during tire flipping sessions. We had all kinds of sizes, but I gurantee if you went all out trying to flip the smaller tires and doing some creative thinking of drills in an interval fashion, you would get tons of work. Our tire sessions left everyone sore from calves, hips, forearms, glutes, traps you name it, and many were throwing around alot more weight in PRs than you (not a knock, just saying just because you deadlift ## means you need a 500lb tire to get work in).
If anyone knows a place in DC let me know though, because Ive moved since my last tire flipping days and am looking for some more!