By the questions you ask, it's clear you haven't gone through the process of calculating pars and variants. And the answers are in the Beyer books for the most part. Maybe "Beyer on Speed" might fill in a few more details about the process.
Either you believe in that daily variant, or you don't. Wrapped up in that is you have to create the best daily variant you possibly can, based on the best par charts you can make. You have to rigorous. 2yos are separate, young 3yos are out of the 3yo and up races, F&M are separate until you know what the adjustment difference is against males. 7F is not a mile is not a mile40yds. Forget the "about" distances; figs for those can be had by using the projection method.
BTW, you do grass races separately. Don't use that "magic" 7F(?) beaten lengths chart for all turf races. The finishes on grass are often very close in reality, and you screw up the ability to assess a horse going from grass to dirt and vice versa by using that bad fix. There will be a lot of pace situations that will throw off the par calculations, so throw out more extreme races when calculating pars, and use as many turf races as you can to calculate pars.
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Is it possible that one race has a higher varient than another race on the same day, even absent extraordinary, intervening weather conditions?
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You mean the rough variant before you calculate the daily variant, I hope? It is surprising the number of days where all races line up almost perfectly. But oddball races should be rather uncommon. If calculated vs. pars charts, how does your variant correlate to (say) the top four finishers (the projection method)? If really different, check the actual race time against video; mistimed races happen often enough. If "higher" means "faster" (some people do the variant in negative numbers), then someone ran a freakishly fast race (and perhaps zero to a couple others may have freaked, but not everyone across the board). And as you might expect, 2yos and young 3yos can throw in a freakishly fast race sometimes. Plus extreme pace situations will affect variants for individual races.
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Put another way, could a race earlier in the day be on a "faster track" than a race later in the day?
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That's actually a different question. You can sometimes have a split variant for different distances or over the day.
Beyer gives examples of that. If you think you need to do that often, either the track is going to hell and Beyers will be useless for a time or you're having extreme weather changes that are so powerful that the track base is being affect - bad news in either case.
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And going one step back, in order to calculate the varient, must you use class and distance pars?
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You can use the projection method, but both ways should be done as a check IMO. One failure that humans make is not compensating for improvement; your final figs start shrinking over time. The projection method used alone will cause this effect unless you're really good at assessing improvement in individual races. IIRC the DRF guys and Beyer add a point to all figs for each month to compensate for this. All I ever did was when calculating the daily variant, I would round daily variants like 17.5 down to 17 (therefore higher figs, reflecting slight improvement) - whole numbers is as close as you can get with confidence. It worked.
Carroll's method is based on one data point for each distance. Very common distances will be well supported by many other races. Not necessarily so for other distances. And track records can be for all time. But I think Carroll requires the track record to be fairly recent. Still, it's not necessarily the greatest horses that hold the track records, either. I thought Carroll was also more about using projection rather than par charts anyway. Tracks will do major teardowns and rebuildings of the surfaces every few years, and when you do Beyer par charts, you should only go back as far as the current surface has existed. And if your favorite track gets winterized with sand, you might think about not using those times in par chart calculations, even perhaps seeing if the winterized tracks have a different profile.
