WB is another story, however: The Builder doesn't tend to have OTP issues into MSP, it's got a full diner, and for a similar example the Silver Star still retains quite a bit of traffic NB out of RVR while the Meteor retains a decent amount SB into RVR. Both have desirable schedules for some folks, after all. This is likely to create some interesting issues...if you get a net of 25,000 folks who want to go WB on the Builder but EB on the state train, that's a headache waiting to happen.
The current Empire Builder schedule is pretty much designed around the Chicago-Twin Cities service.
I wouldn't be surprised to see a state-run train running very close to the same timeslots, maybe a couple of hours difference. Think about it this way:
(1) The main market is Minnesota residents visiting Chicago, not vice versa.
(2) The timetable is too long to serve day trips. (And you can't run the service with one trainset.)
(3) You don't want to run overnight.
This gives you two options for the westbound:
(A) depart afternoon, arrive evening
(B) depart morning, arrive afternoon
And two options for the eastbound:
(A) depart morning, arrive afternoon
(B) depart afternoon, arrive evening
Given that you're serving people from Minnesota visiting Chicago, you want to maximize time available in Chicago on a short trip, so you pick (A) both times, and you have a schedule which is pretty much the current Empire Builder schedule.
If the MSP train runs in close to the same slot as the Empire Builder, this is going to cause much less complaint from BNSF and CP, who can "fleet" the passenger trains if they're running on time.
Alternatively, if there is a standalone train on roughly this schedule, this allows the Empire Builder to move to a different schedule. It could be one more focused on its western connections: departing later eastbound, departing earlier westbound. Or it could be one more guaranteed to make Chicago connections: departing earlier eastbound, departing later westbound. Either way it would probably provide worse MSP-Chicago service.
So I don't think there will be much schedule competition between a new train and the Empire Builder for MSP-Chicago service. Some people may wish to take the Empire Builder in order to use the dining car or sleepers, true. I don't think this is going to be a huge group of people, particularly if the prices for the Empire Builder are kept slightly higher than the new train on MSP-CHI.
Regarding Minnesota's potential willingness to let Wisconsin "freeload", I looked at the PIP at the top 10 Empire Builder markets and what would happen to them:
Chicago-MSP (8%) -- new train
Chicago-Seattle (4%) -- Empire Builder
Chicago-La Crosse (3%) -- new train, and this benefits Minnesota (La Crescent)
Portland-Pasco (2%) -- Empire Builder
Chicago-Portland (2%) -- Empire Builder
Chicago-Winona (2%) -- new train, and this benefits Minnesota
Portland-Spokane (2%) -- Empire Builder
Minot-MSP (2%) -- Empire Builder
Chicago- Wis Dells (2%) -- new train, first "freeloading" from Wisconsin
Portland-Whitefish (1%) -- Empire Builder
So, just looking at the top 10 markets, 15% of the Empire Builder traffic would go to the new train, and of that, 13% would be Minnesota-benefiting traffic. Of course, I assume the standalone train would do better than that, but it goes to show what portion of the new train's traffic would be Minnesota-centric.
A plausible one-a-day service could be operated with 2 trainsets. If Minnesota decided to tag onto the bilevel order using the existing configurations, each would probably start with 1 locomotive, 1 "cab/baggage" car, 1 "cafe/business class" car, and 1-2 coaches. That's 6-8 cars and 2 locos -- not a lot. Enough to scrounge up by paying equipment charges to Amtrak, even. Or to Illinois, if some of its services take longer to get going than expected (which they might).
I could see Illinois paying for part of the service even if Wisconsin didn't; and if it absorbed a Hiawatha slot, I could see Wisconsin paying something even under Walker's government. The main obstacle in Minnesota is a retrograde group of anti-rail legislators from certain suburbs, and while that's an obstacle, I don't think it will last.
This leaves the obstacle of how much ransom CP will hold Minnesota up for -- if they demand a king's ransom, obviously, the train won't happen. We won't find out until the study is published, and maybe not even then.
Marketing would certainly be necessary... but also straightforward. I think it would be worth being honest and advertising "This train starts in St. Paul -- so it will leave on time."