I've rented from Alamo, Thrifty and Dollar at LAX and all three have been equally pleasant experiences. Actually, Thrifty was the best because their facility is a lot closer than Alamo's (I swear it was a 20 minute ride on the shuttle bus all the way out to Alamo's lot). The personnel at all three spoke equivalent amounts of English (i.e. not a lot). Truthfully, with all of my rental experiences around the country, I've found very little differentiation between companies (there's more difference between individual locations than the companies themselves). The frequent renter programs offer different perks (Thrifty's gets you free days, National's gets you status and upgrades, some let you pick your own car out of an aisle, etc.), but for the basic rental itself, there's not much difference, and LAX seems to be no different.
The only difference seems to be Enterprise, probably due to their very different method of staffing: they only hire college-graduated type-A personalities who are all aspiring to someday be executive vice president of the company. This leads to a much more professional staff (i.e. not just low-end wage earners or college students) but also one that is very, very, very pressured to make the company lots of money (high sales make you look good and more likely to get promoted), which is why they pressure their customers so much to buy coverage and upgrade vehicles.
Even working in the industry, I've given up hope trying to figure out any sense in rental rates. IMHO, the real reason there are so many weird things like this is because the yield management people are not really organized and just making it all up as they go along. (In fact, that seems to be typical of the whole industry--it's more of a game than a serious business...). Somebody probably just randomly set that good weekly rate to expire on Wednesday and never bothered to check the rates for the next day. I sincerly doubt it's because the minivans are more popular on Thursday than Wednesday...
If you want to, you might be able to book the reservation for the Wednesday but then call the location directly and ask to move it to the next day; they might be able to do so without changing the rate. Since our franchise location's computer system is completely independent of the central reservations system, we can (and do) do this all the time, but since LAX is a corporate-owned location whose computer system is tied with reservations, it may change the rate just the same as if you called the reservations center. (I did a little digging online and found this number: (310) 645-1881. The 877 number listed for the location at thrifty.com actually forwards to the central reservations line in Tulsa, so use the above number to actually talk to someone in Los Angeles.)