This is exactly why you need a tax professional. You're linking to an article that is related to whether or not you can "write off" bad/uncollectible debt; it's not relevant. The first sentence most likely "disqualifies" you from the article's contents entirely -- you're probably not a small business that is using accrual-basis accounting, it sounds like you may not even have an entity at all (which is fine).

You need a tax professional (or even a semi-pro); in the interim, I'd suggest solely relying on what you read on the IRS website.

Generally speaking, by default you are likely cash-basis -- but yeah, this income & especially with "high variance", get with a professional. If nothing else, figure out whether you actually need a loan or not before applying/asking for one...

IANAL/IANA-tax-pro -- but you almost surely do not need a loan.

I don't know about the USA, but in some countries you can claim a "reserve" for accrued but unpaid amounts in some circumstances. Worth talking to an accountant to see if that's a thing in your case. (Note, there's also "reserve for doubtful accounts", which is if you're not sure if you're going to end up getting paid. It sounds like that one wouldn't apply; I mention it just to be clear that I'm not talking about that sort of reserve.)

There is no situation in America where you need to pay tax on a general invoice within two weeks of receiving payment.

Both of which allow you to net out expenses and only be taxed on profit

I think that if the OP were an accrual basis taxpayer they would already know how to handle this situation, since accrual-basis accounting is opt-in for individuals and S-corporations.

Note to other reply: estimated tax payments are made during the year. While you can net out expenses, if income is distributed unequally during the year this can result in penalties/interest if you underpay in one quarter based on the liability as calculated after the year ends (to complicate things, there are multiple ways to estimate tax payments during the year to account for these situations).