My gut understanding would be that because ORD-MSN-ORD is for all intents and purposes a round trip (even if it is nested within a larger one way itinerary) and that because the eVIPS are used for the for up two three segments on a one-way trip then it would not work. The old six segment VIP upgrades would have worked, as what you essentially have booked as it appears to AA is an open jaw (HNL-LAX-ORD-MSN/MSN-ORD-LHR).

The other thing that might be affecting this is the stopover in MSN, since it doesn't appear that you have any stopovers in other cities, and my understanding is that anything more than a connection (in this case the stop in MSN) would allow you to use one eVIP for the legs on either side of the itinerary (i.e. HNL-LAX-ORD-MSN or MSN-ORD-LHR); in order to get both parts (pre and post-MSN) upgraded you would need two eVIPs. I think however even if you were to cut out the ORD-MSN-ORD portion and just go HNL-LAX-ORD(stopover, where you buy a separate ticket to MSN)-LHR, you would still have to use two eVIPS because of the stopover in ORD. Perhaps not, but last time I talked to EXP line this is what they told me (but I will apologize ahead of time if this is incorrect as I use my eVIPS for simpler itineraries that never include the stopover). Another FTer with stopover experience using the eVIPs will comment and you may also want to check the stickies or the eVIP rules.