I think the "sleeper service" concept will offer the OP the best of both worlds. You can have a small bite in the lounge, and then have a salad / small plate / dessert on the plane. Service on board will be soon after take-off (rather than lasting 2-3 hours as happens on Westbound out of LHR) which gives flexibility to rest & relax and get some sleep too. Don't underestimate how tired one can be after the airport experience and a couple of whiskies on board - having a few hours' sleep at 20.00 Eastern time may seem a nice idea once you get there.
The reality is that if you ask, crew can deliver on a "sleeper service" a condensed meal experience which isn't so dissimilar from the "full" CW product.
I would strongly suggest the OP skips breakfast on board - maybe just a pastry and a cup of tea / coffee to wake up, and then go for a shower and very good breakfast at the arrivals lounge in Terminal 5 (which is landside after arrivals, up in the lift) - the Arrivals lounge is genuinely a great product and one of the best features of Club World overnights.