Tracking taxable reimbursement in double entry accounting with cash accounting (as employee)

Question

Let's suppose we have the following events

• 2021-12-15: I paid $1000 rent from my checking account.
• 2022-01-15: I received $1000 in my checking account from my employer as the housing allowance (suppose this is taxable).

I have the following four accounts

• Income:HousingAllowance
• Assets:CheckingAccount
• Assets:AccountReceivable:HousingAllowance
• Expense:Rent

Based on https://money.stackexchange.com/a/35520/99152, what I could do is:

(+ is debit and - is credit)

2021-12-15 * "Rent"
  Expense:Rent                                 1000.00 USD
  Assets:CheckingAccount                      -1000.00 USD
  Assets:AccountReceivable:HousingAllowance    1000.00 USD
  Income:HousingAllowance                     -1000.00 USD
2022-01-15 * "Housing Allowance"
  Assets:CheckingAccount                       1000.00 USD
  Assets:AccountReceivable:HousingAllowance   -1000.00 USD

This is perfectly fine except for one problem: now the Income:HousingAllowance is logged in 2021 instead of 2022. But in reality the income would be counted as the taxable income in 2022, not 2021 (since we are doing cash accounting).

What I would ideally want is

2021-12-15 * "Rent"
  Expense:Rent                                 1000.00 USD
  Assets:CheckingAccount                      -1000.00 USD
  Assets:AccountReceivable:HousingAllowance    1000.00 USD
2022-01-15 * "Housing Allowance"
  Assets:CheckingAccount                       1000.00 USD
  Assets:AccountReceivable:HousingAllowance   -1000.00 USD
  Income:HousingAllowance                     -1000.00 USD

but this is not balanced.

Is there another account we could open to balance these entries, or are there any other ways that would allow us to track the rent, the income, and the account receivables at the correct dates? Thanks!