Prebans I'll try to answer what I can about your circumstances.

1)  CCW is a hit or miss situation depending on your County, as was stated before, and won't change before you get up here.  I live in a non-issue (good old boy system) County but will be visiting the Sheriff this fall/winter and asking him if he wants me to be carrying Class 3 firearms around without a CCW?!  Others in our Corporation said he should see the light after that statement.

2)  As was stated above you'll need to form a Corporation in Iowa to have your Class 3 license transfered to this State.  I don't think I'll need to tell you how long all that paperwork will take between the State and the BATFE.  You'll set up your Corporation and its members (wife, etc.) and then transfer your license to your new address up here and wait for that updated license to arrive.  So you'll need to know what your address is before you change your FFL's address which means you have to check on the most important aspect...ZONING.  As you're aware of zoning plays a key part on where you can set up your Corporation/FFL(SOT) without having to have an actual storefront and regular business hours.  Ideally you'll find a place to live out in the country and in an unincorporated area that has no zoning requirements.

3)  I'm not sure if you're just coming up to Iowa to be a student or if you're going to be teaching and staying awhile.  While you're waiting to find a place to live and waiting for your Corporation to be registered with the State all your Class 3 firearms will have to stay down in Arizona.  If you keep your address in Arizona that your FFL is listed at you can keep everything down there as a dual-state-resident if you're only going to be up here for a year or so and plan on going back down there to live after going to the U of I.  Lots of variables as I don't know if you operated out of your home or if you had a store front down there in Arizona, I do remember a year or so when you announced that you were going to becoming a dealer but I don't know to what extent you became.

4)  If you gave up your license you would have to give up any Post-86 Dealer Samples you have in your FFL but you would be able to keep Pre-86 Dealer Samples and Transferables if you left them down there in Arizona at an address known by the BATFE and stored in a way that only you have access to.

I'm no expert on this field and don't know your situation completely but I hope this helps you out a little bit.  If you were to place this question on the M-16/Auto forum you would get answers from others who have gone thru what you're asking about and have more experience in this area than myself.  Good Luck on whatever you decide and feel free to ask any questions you may have!

ETA:  Having reread your post I see that you're putting in an application to the law school so that rules out you being a teacher.  Also I see that you stated next year as when you'll be attending if you get selected, you would still need to check on zoning where you're going to live and have a lease/mortgage on that address before you can submit paperwork to the State about forming a Corporation and to change you FFL address from AZ to IA.  Basically if you want to have everything set for next school year you'll need to have set up an address for your paperwork/application.

I'll double check on the forming of a Corporation up here to form a FFL/SOT.  I know of only one other FFL/SOT here in Iowa (currently operating) and they're in the Des Moines area as well and they are set up as a Corporation as well, actually they were the first to form a Corporation and bypass the ban on private ownership of Class 3 firearms in this State.  Yes, Iowa used to be NFA friendly but a law was passed that banned them and there was NO grandfather clause allowed...that means there are "legally transferable" firearms owned "illegally" in Iowa by citizens who have them stored away so no one can find them until their descendents find them as they're getting their estate ready for sale.  I know of two cousins up in northern Iowa that are Class II manufacturers (as well as Superior Arms waiting on their paperwork to come back) and was just introduced to another manufacturer last weekend who specializes in Thompsons...he just started in August and I believe he had four Thompsons there that he had built and they were sweet!  He had a .22lr Thompson that ran great and may have him build us up a Post-86 .22lr Thompson as well as trying to make a Post-86 sear pack for my PPS-50.

Since you are a current FFL/SOT I will ask around and see if you could just change your FFL/SOT address (pending zoning approval/lack of zoning) from down there to up here without forming a Corporation.  I'll be getting back to you on that!

*** UPDATE: ***  
I spoke to someone MUCH more advanced in Iowegian NFA knowledge than me and you do NOT have to have a Corporation to have your Class 3 FFL/SOT back here but we do it back here as it prevents someone from suing for more than the Corporations assets (in case of accident) which makes all the spouses happy that they won't end up living down by the river in a cardboard box.  You would have to find an address in the Iowa City area that would be zoned so you could operate your FFL out of your home or live in an outlying area that has no zoning restrictions.  Once you find an address that would work you'd send in your paperwork to change the address of your FFL which CAN take a long time believe me.  At that point you can do one of three options:
1)  Keep your inventory locked up in a neighboring state
2)  Keep your inventory locked up at your parents place in WI
3)  If you'd like you can keep either: one, some or all (unless it's a REALLY big collection or they're all bulky belt-feds) of your inventory at our locations (ours and/or the other Class 3 FFL/SOT in town) which would be temporarily entered into our books until your change of address is returned to you.  Advantage to you is that you could shoot your firearms in this state (as long as a member of the FFL that is storing that firearm is present) and advantage to us is that it shows a positive flow of incoming inventory to our FFL and then being transfered back out to you once your FFL change of address comes back approved.  Your firearms could be kept in locking cases that only you have the key to (I believe that is legal even though it's in our FFL's "possession") which would prevent any notions of use/misuse on our part.  If you'd only want to keep a couple machineguns that you shoot the most often and store the rest at your parents or the neighboring state that would be up to you.  You already know that you can "store" at either your parents or the neighboring state (providing it's NFA friendly) as long as you are the only one with access to their locked status.

Just thought I'd let you know what I found out and give you some more options to think about...as if you didn't have enough already!