To make a meaningful comparison I think you would need to look at availability through Continental and Delta on the same dates.
To take the JAX-LHR example there should be one-stop service:
via ATL on DL
via DFW on AA
via DTW on DL
via EWR on CO
via IAD on UA
via MIA on AA
via MSP on DL
via ORD on AA or UA
via PHL on US
I based this on a list of nonstop destination from JAX published
here, and my recollection of who flies non-stop to London from various markets. Accuracy not guaranteed

.
Aeroplan should have access to flights operated by CO, UA, and US. You might try checking availablity for each segment separately to verify that their site is constructing the best connections.
Also, AA and B6 (JetBlue) have a partnership which
might allow you to fly to BOS or JFK on JetBlue and then internationally on AA, but I do not know if this partnership extends to award redemptions.
Hi Dennis - I have done a lot of cross-searching - particularly on Wednesdays in January when we having a northeaster

. I pretty much know the best flights to lots of places. But the good routings on the metal with lie flat seats just aren't there for the most part. Except on perhaps a day or two during a month - with no return flights available. Took a look at Aeroplan as well a day or so ago. Same result. Note that when I search - I search not only from JAX - but from major gateway cities. When we got BF reward tickets to Tokyo - they weren't available from JAX. "Bought" them EWR to Tokyo and paid for relatively cheap flights from JAX to EWR out of pocket.
If we have the energy next year - I would like to go to China - especially now that the new high speed rail between Shanghai and Beijing has opened (article about it in the WSJ this week). I will see what's available in terms of getting there later this year. Finland and Sweden are still on my to-do list - but not until they get some luxury hotels (they currently have 3 star properties at 5 star prices).
Heck - worse comes to worse - I'll pay for the tickets. We've been saving money for our older years forever - and I think we've reached them

.
FWIW - your routes are pretty accurate. But why would we fly through places like Dallas or Minneapolis to go to London? Kind of have to laugh at this. Because when we flew to Tokyo - I thought the easiest/shortest would be due west through LAX. Didn't know the polar route through EWR would be a whole lot shorter. I guess I - like a lot of people - am geography impaired. Robyn