Paid invoices go to Accounts Receivable, and once there they no longer show up as Income on my P & L. Why?

What I see is Not Correct. Let's review:

You charge a Service, so that is linked to Income. This will control the flow of the data to accounts.

You use it on Sales Receipt = the date of the sale is also the date of the payment.

Or, you use it on Invoice = This is Income, but not yet a Paid sale. This creates the AR. Your Item is not the AR. The function of using Invoice creates an Unpaid sale, which is AR.

Then, you get paid; this is Not a Deposit. You should never see DEP. This is a Payment, when you used Invoices. Or, you already got the funds from the Sales Receipt. The only time you would see DEP is if you Batched all the payments and your sales receipt by sending the payment data to Undeposited Funds, to be held until the banking shows up.

So, it is like this:

Sales invoice (income here) ==> AR ==> Payment arrives ==> Held as UF ==> Banking happens

That's why DEP never shows Engineering Fee Income. That is Settlement of the sales, and not your Income event.

Let's break this down a bit:

"At which point QB puts that money in A/R."  I wish it didn't, I wish it could just corroborate with the bank/Paypal deposits."

It is Neither AR nor Banking; you need to edit your Charge items and link them to Income and let QB move existing data for you.

"Worse still, these transactions are hidden in my A/R, as my P & L reports don't see them as income."

You will always see Invoice as the Transaction Type that creates Income. But the income doesn't show on Cash Basis for unpaid sales; it shows on Accrual Basis for the date of the invoice, even if Never paid. For cash basis, it shows that invoice for the date of the Payment, on Cash Basis, but you still see the Invoice. The invoice (the Sales) is the Income transaction.

"I wish it didn't, I wish it could just corroborate with the bank/Paypal deposits."

If you use the banking download, never let this Add to the file; these are not DEP, if you never yet processed payments. They are Matched to open invoice. Or, Matched to the amounts still sitting in UF.

And you should be managing PayPal as its own Bank account in your system, if they hold your funds and you incur fees there. That way, a sales receipt or Invoice Payment would post to the PP bank, not to US, because they are posted Individually in reality. Bookkeeping matches reality. Then, settlement to Real Checking from PP is a Transfer; this is not income again. It is you, moving your own funds around. Your PP fee is a Check from the PP bank. You use the PP statement to reconcile your PP bank in this file.

"P.S. I use the cash method (I tried accrual but it seemed more problematic and unnecessary, I'm a sole proprietor)."

You run the Reports on Both Basis, to keep on eye on things. You are using invoice to Anticipate payment will arrive, because you have in fact charged the people. That is fine.

Cash or Accrual is a Tax Reporting perspective. In the accounting, we use the tools that meet our needs.

I have attached some images that are from PC desktop, but they should be helpful to you.

"Your income account is not set correctly. Check the box "this service is performed by a sub contractor" Now you will see where you can assign an expense account on the cost side and an income account on the sales side."

You would do that when this is something you Incur, Charge, or for Both events. Otherwise, all of your Fee items are linked to Income. You showed an image with one linked to AR and this is the Error.

Check the items used on the invoice, the cost side should be assigned an expense account or COGS, and the sales side assigned an income account.

Right here: "Why would I check that this service is performed by a subcontractor when it’s not- it’s performed by me, the sole proprietor?"

It doesn't have to be checkmarked, then. But you NEVER link an item to AR; you are going to put it on a Sales Receipt, or an invoice, and that item is your Income. Using an invoice is creating AR, already.

"And what should the expense account be?  My main biz checking account?"

You seem to be confusing Source of funds and the Reason or the Why funds left. I am giving you an attachment that is a handout I use to teach the Basics of the account types. When someone mentions assigning to Income, that means Revenue, not Bank. Bank would be the Destination, but Income is the Reason. When someone mentions "that is an expense account" that means Expense, not Bank. Bank would be the Source of the Spending and "office supplies expense" is an example of the Reason funds are being spent.

"I mean, I can’t ever see using an invoice for “purchases” as I’m not that kind of a biz.  I’m just a recording studio owner who bills artist clients through invoices."

Let's review: you show using DEP for income; that would be Sales Receipt using that same Service item for what you did. The same thing that you would list on an invoice, is listed on a sales receipt.

Sales receipt = I am also already paid for this date.

Invoice = I am charging them, it isn't paid yet, and the funds will come separately and later.

Both of these are your Sales processes. Both of these result in Funds to Banking.

"The fact I have to lie about it"

It's not a Lie. The recommendation was to set it up as a Provision. You don't have to do anything anyone tells you, here. We are explaining the tools. The point is, never link to AR because you overlooked Income. That item for "what I did for you, that you owe me for" is your Income activity.

"and say I’m using a subcontractor and link it to an expense account leads me to believe the QB Invoicing system is not for me."

Do not get out of control over this. A text based forum means we work together and back and forth, to narrow  down functions you use, how you use them, functions you didn't realize work better for you once we learn what your needs and operations are.

"Especially if invoices can’t “shake hands” with my downloaded bank reports as qbteachmt suggests"

Your Banking info is Verification. A Sales Receipt or a Payment against in invoice will be part of the Banking. We all use these tools.

You must be entering something incorrectly. 

When you create the invoice, and before the client pays  that is when the money should go into account receivables. When it is paid, and once you match the bank transaction to the open invoice  it will remove the balance from receivables. The accounts receivables is an asset so it was already on the balance sheet before you got paid . The payment only will affect your cash but you wouldn't see assets increase further. The cash asset would increase and receivables asset will decrease for a zero net change there..