I voted "other"
For starters, I wouldn't individually bag the fish, I'd species bag them (one bag of black fins, one of red eyes, one of x-rays, one of corries, and a plec bag). The tetras/corries will be much happier in with their mates than sloshing about on their own. I strongly advise you do this.
What you don't say is how far you'll be moving. If it's over an hour tank to tank, then come back as you'll need to revise the condions under which you must transport the fish.
The rest is personal preference: I would get the 55 set up in advance at the new place with brand new gravel and plants, and filled with water. This is a great opportunity to get your new tank set up as you want it instead of hotch-potched from other bits.
Then I'd move all the fish from your 20 & 10 tanks (treated exactly as Wolf says), along with the filters and heaters from both tanks (the fish don't look incompatable at all), and whack them all into the new 55. Bear in mind heating the water too, don't chuck them all into a 55G ice bucket. Consider this as a priority, you could do with the temperature being acceptable when you arrive at the new place. Acclimatise the fish properly too, don't just pour them in.
Move the bettas in their tanks with half the water removed- those little pint pots shouldn't have a problem with the weight (take out any decor if you're worried).
Then I'd move the other two tanks at my leisure, completely empty, and thoroughly clean them (and the gravel), before positioning them as I wished in the new home.