Apparently my method is a mix of those listed in the text.

I'm in a similar situation as OP, some of my income is irregular. So my monthly budget isn't directly based on the last month income, I use the average of the last six months, relying on a checking account for that. (I keep it with enough money to last me one or two months.)

Then I split that budget into four categories:

• savings - I aim for 25%. Into the saving account it goes.
• monthly fixed expenses - periodic, somewhat predictable, monthly. For example bills, cornmeal and rice, cat food, etc.
• variable expenses - they're necessities like the above, but there's some wiggling room. Like, if necessary I don't mind eating eggs four lunches a week and walking instead of taking a bus, but I'd rather not to. Usually split into four weeks, so I expend it gradually.
• "fluff"*¹ - avoidable expenses that I still want for some reason like "it improves my mood". Things for my hobbies, going to a restaurant, buying nicer clothes or hardware, etc. Unused fluff gets transferred to my savings account in the following month.

Then here's how I address some complexities:

• periodic expenses for things that I buy every few months (e.g. gas canisters) - I include a fraction of them into the monthly fixed expenses, and only remove the money from the checking account when buying it
• erratic but large expenses (e.g. house repairs) - I usually "borrow" this money from the savings, then "repay" it in the following months, as a fixed expense*².
• high income multiple months in a row - I cap the budget and send the overflow to the savings.
• low income multiple months in a row - cut down fluff, then reduce variable expenses, then reduce monthly fixed expenses, then reduce savings, in this order.
• really low income multiple months in a row - if really necessary I borrow from the savings, keeping in mind that I'll need to repay myself.

Notes:

1. The actual name that I give to this category is "imposto das lombrigas", or roughly "roundworm tax". That's from from my family jokingly referring to cravings as "to have roundworms for [something].
2. Some people might use a credit card instead for that, to build credit; that also works, but it depends a lot on the government that you pay taxes to. I do have a credit card but I tend to avoid it, as often there are discounts for paying things in cash.