Unfortunately, OP has no status so probably a non-starter but at least worth a call.
The day time flight from ORD has availability on 8/28, 8/30, 8/31 but only 1 seat on 8/29. An early start from BOS and you get in late-night to LHR (so would have to overnight in LON), so not exactly brilliant. There's virtually nothing available coming back.
Is buying an economy ticket and paying to upgrade (miles + co-pay) of interest? If so, the direct BOS-LHR flight on 8/29 is C2; coming back on 9/5, the early LHR-ORD is C3 or the direct LHR-BOS on 9/4 is C4.
It may be, although between the copay and the
british gov't upgrade tax...! I hadn't seen the upgrade inventory because apparently ExpertFlyer masked it out when my end destination was EDI - LHR-EDI is flown on a BA codeshare. I guess you have to look by segments to see it.