Honestly, I think you're SOL this year by now if your budget is that strict. I see ORD-MAN for 7,626 miles for $1,036 on Dec 29th, then ORD-MIA-SJU is $655 on Dec 24th for 4,484 miles. But that still leaves you short by 2K miles, and you're already over budget by then.

ETA: Example, ORD-DFW-PHX is $508 on Dec 31 for 3,332 miles, taking you up to $2,199 for 15,442 miles.

ETA 2: ITA was giving me hiccups earlier, but now ORD-RDU-LHR is coming up on Dec 29 for $1,019 for 9,010 miles. That plus SJU would put you at 13,494 miles.