There are a lot of variables to consider, but I think you've come to a pretty good assessment so far. Here are my thoughts:
Housing/lodging/etc.
If you can find a friend who has family or a place to crash somewhere in the Plains/Midwest, that can significantly cut down on costs (even cutting out 5 hotel stays in a month can save $250-$500). I was going to post my budget numbers from this year, but it wouldn't be fair, since I spent some time in May with my Aunt in Oklahoma City and would occasionally crash at a fellow chaser's or friend's house for a night. As for hotels,
I've compiled a list of nice hotels/motels in chase territory that are mostly under $75/night (many $50 or less) and there are far more than the ones I have reviewed. If you chase with a partner, you can increase the budget, but split a room two ways. Do keep in mind that budget hotels/motels can be very hit and miss, so always try to read reviews prior to booking or check out a place in advance, if time permits.
If things work out, sometimes you can book a particular spot for a few days in a row, maybe even a week. By doing this, you can often save even more (I booked a motel in Kansas this past June and received 50% off for booking multiple nights).
Verdict: I would say $75/night is a safe estimate (cut in half for two people), but you can easily do better with some research.
Vehicle/gas/food
The vehicle you chase in is huge, with respect to gas milage. My vehicle (Toyota Camry) averages 35-40 mpg, which can be close to twice as fuel efficient as SUVs many chasers use.
The tradeoff is that traction on dirt and other roads may be compromised. For oil changes, if you get a relatively new car to rent (or otherwise use), I believe oil changes are only necessary every 7,500-10,000 miles.
I don't mind keeping food costs to a minimum. A lot of hotels (even the cheaper ones) will have something to eat for breakfast, if not a full continental breakfast. I pack energy bars and fresh fruit and lunch/snacks. During most chases, you may not have time for dinner, but when there is time, I try to keep the fancier meals for celebrating after a good chase. It is tempting to try out restaurants in different cities around the country, so I'm not sure how realistic it is to really keep the food budget down to a minimum. (I end up splurging more as the chase season goes on, plus your body eventually wants something more substantive, especially if we're talking about several weeks to a month or more)
Going back to fuel economy - this is something that goes "under the radar." The speed limit on most roads across the Plains ranges from 70-80 mph and you'll start losing fuel economy substantially, especially over 70 mph, in most vehicles. If it's a travel day and I don't need to rush to get anywhere, I don't mind driving close to 65 mph to save fuel costs. It may not seem like much, but when you drive tens of thousands of years every chase season, it does add up. I've gotten over 700 miles on one tank of gas, but struggle to get over 500 miles if I'm driving at higher speeds and/or doing a lot of city driving.
Verdict: You may want to compromise for a vehicle and get something that's reasonable on gas, but also handles well in dirt/muddy conditions/etc. GasBuddy is a great app to find cheap gas. For food, I find it's best to buy things prepackaged, it's cheaper, saves time (less stops) you won't be tempted to eat out (or stop for junk food) if you have food in the vehicle.
Driving distances
I think the 500 miles per chase on average is a fair estimate. While you may get some setups where the same state or general area is targeted a few days in a row, there will be days where you may have to drive 500 miles to get into position and then a few hundred miles more that night to set up for the next day. (I've chased in Minnesota and needed to get to central Illinois the next day, or started in New Mexico and went all the way up to the Dakotas for the afternoon) An average vehicle may get 25 mpg (low estimate), so do the math according to the vehicle.
Verdict: Plan on 500 miles per chase day, on average.
Vehicle repairs/other costs that can come up
If the vehicle is newer, repairs will probably not be a big issue. However, keep in mind that flat tires can happen at any time, especially when you may be driving through questionable roads and debris. The longer distance associated with regular chasing may increase your odds of getting a flat. Busted windshields from hail are another consideration. Although I do my best to avoid large hail, I've been dinged even while a few miles away from a storm. I've also been hit by rocks from other vehicles in back-to-back chase seasons. Good car insurance will cover most or all of the glass replacement cost, but if not, that cost is going to be at least a couple of hundred dollars, per instance.
Verdict: Consider car insurance and avoid large hail, if possible.
I think $2,000 is a generous budget for a month if you split the cost with another person. It also helps if you're with someone who's either familiar with the area, and/or an experienced chaser. Then you may save even more (less out-of-the-way driving, knows good/affordable hotels, may have a place to crash on occasion, etc.)