The "20% per 100'" rule of thumb you found there isn't very good. It's excessive for short distances and insufficient for long distances, and this is the latter. Anyway, Voltage Drop Calculators exist so I consider the rule to be functionally obsolete. Remember to select aluminum because it won't, and 3% is a salesman's suggestion.
However, you say you will be running this continuously near 80A. That sounds like something a novice would say - but you may well know better than I. OKAY... think about it. What does 1% voltage drop cost you? 80A you say? 1% of 80A is 192W or 4.6 kWH/day. 1681 kWH/year and at 12 cents a KWH, $200/year. Over 10 years, $2000. Obviously if your load is partial-day, (e.g. a big solar array that really only hits its number 1/3 of the time)... you should factor accordingly. If I were you, I would actually run several Voltage Drop calcs between 1% and 6%, and compare the cost of wire for each scenario, vs the cost of wasted electricity, and see what makes sense for you.
If your loads are predominantly 240V, remember that voltage drop is your free choice and not mandated by NEC in any way (except you can't plan for voltage drop over 10-ish percent, for fault clearing reasons deep in Article 250 arcana) . As such, nobody's going to write you up for using the minimum legal wire size of #1 aluminum for neutral. To get voltage drop on the neutral, run through the voltage drop calc again, and give it neutral "imbalance current"... and then, divide by 2 (since it's giving you round trip voltage drop, and you only need one-way).
is it possible to reduce the wire size for the run by stepping up from 120v
Wait. Did you say 120V???? Remember that thing I said about novices? It's movie time: go watch this Technology Connections video on how our power is actually 240V. If that video is news to you, then you should probably ask another question, giving detail about your loads and asking how to figure balancing and sizing. This could be a total game-changer on wire cost.
Is it possible to reduce the wire size for the run by stepping up from 120v to 480v and then back down at the other end?
Absolutely. However this is serious "pro tier" stuff. And you'll have to get lucky on Craigslist to really save that much money; otherwise transformers this size are not cheap and may well cost more than the heavy wire, since aluminum is our very best friend at these large feeder sizes.
So yes, you obtain two transformers of appropriate kVA (VA is a funny way of saying watts, and k means thousand). For 80A @ 240V that sounds like 20 kVA to me. The typical popular transformer you're likely to find on Craigslist is 240/480V on one side and 120/240V on the other side. You wire the transformers up "back to back" primaries facing each other, so the primaries jumpered to 480V are connected directly to each other. This is where you must be very careful with construction methods so the conduit is literally going straight down out of the transformer and pad, a continuous uninterrupted run to the other transformer pad and straight up into the other transformer. No going through extra boxes, no pull boxes, no intermediate stops - you really, really do not want amateurs trying to open up boxes and mess with this, because it ain't what they think it is. If they open up the transformer enclosure itself that is plainly labeled "240/480V", then they deserve their Darwin Award, but give them no other temptation. Keep it very simple, neat and pro.
What about overcurrent protection for this 480V circuit? It is provided at the source by the 240V breaker feeding it.
Now you are doing your voltage drop calculation on 50A @ 480V and you may find more pleasant wire sizes come up. Whether you save enough on the wire to justify buying two transformers, I cannot guess.
Again this is pro-tier stuff, and is an easy way for a sophomoric K.I.A. (know-it-all, but the other thing too) on the wrong side of the Dunning-Kruger curve to win a Darwin Award just to save a few bucks on wire. Pro advice is essential here. There are lots of missable details.
At the secondary at the shed, you jumper the 120/240V side for 120/240V split-phase. Feed that into a MAIN panel with a 100A breaker. This will be a main panel since it is a seprately derived service. Neutral is bonded to the ground to the ground rods at the first disconnect past the transformer secondary.