Quick transporation is a priority for our family too, but I can't answer your poll directly for several reasons.
All things considered, my favorite mod is probably CSR, but it is not be the best for transporation.
Second, it depends what you mean by 'best transportation.' An important variable is the time of day you plan to go back/forth between the parks.
If you go strictly at peak times, then I think POFQ is probably the best mod. If you go in the middle of the day, then I think it's a complete toss up. Most of the mods are quite large and mid-day the buses will loop around the whole resort. So even if the bus doesn't get full - it takes a while. POFQ's bus makes the loop around POR - so that's one of the WORST transits. Once you finally depart the resort, POR the closest mod to MK, but overall they are all about the same if you plan to hit all four parks over your visit. (Over the week the differences will average out).
Both POR and POFQ have a boat to DTD. If you like variety, then those resorts are the best because otherwise all other transportation from mods is via bus.
The only time buses don't loop around the whole resort is sometimes during peak transporations times ( around 8:30am, dinner, park close). At POFQ, the bus gets full and heads to the park directly during peak times of the year, or it may stop only at the main bus stop of POR. (Later in the day though it may loop POR to let people off the bus, even if it's full)
If getting to the parks quickly is your MAIN priority, I'd suggest a value resort. They actually have faster buses. If you are going during a non peak time (not a school vacation week), then I would say Pop has the fastest transportation - so long as you don't mind full buses (otherwise the ALL Stars). The resort is so large that buses are pretty much continuous all day from Pop. The only time this is a problem is getting back from a park at park closing. The Pop century buses ONLY stop at the main bus stop - no other stops or resorts - so they are very fast. Teh All Stars are a close second. There is enough demand at all of them to keep continuous busing all day (most WDW resorts have 30 minute intervals mid-day). At All-Stars, you have the option of getting off at any of the three stops, and it's pretty easy to walk between resorts. ASMu is the middle resort.
Another important tip - at the mods there are no bus queues. The bus stops are covered, but they are kind of a mob scene sometimes. The main stop is the most crowded, but also the first stop (after that, at the big mods the bus is usually full during peak coming/going times). Sometimes the most agressive folks board ahead of those who waited the longest. At the vlaues, you LINE up at the ONE resort bus stop, so getting on a bus is much more orderly - at least at peak times, but the stops aren't covered and there aren't any benches in the queue like there are at the covered bus stops.
One last thing to consider - is not JUST the buses - but how much TIME you spend WALKING within the resort. Most folks eat breakfast at their resort most days - and/or take their resort's main bus stop during peak times. If minimal walking is a priority to you (again, thinking speed) consider a preferred room location or POFQ. Personally, we found a first floor preferred room at Pop to be the best in the mod/value category. Otherwise, you can lose a LOt of time walking across the resort. Say if you decide to go back the your room after breakfast- - just to drop something off or grab a jacket - it may well cost 25 minutes at the bigger mods.
You may also qualify for a discounted room at the Swan. The Swan is close to both Epcot/MGM, has deluxe accomodations, and at $199, is not THAT much more that a moderate. You can't get the dining plan or ME at the Swan, but if you already planned on a car and meals oop, then it's a great choice. It's fast to Epcot and MGM, and the buses to MK or AK most of the day only stop at the Dolphin AFTER that go to the Swan (so you get a seat, the Doplhin folks don't.)