You may want to find out when DC considers K-1 income to be earned. For Illinois it is on the last day of the PTE's tax year. So for calendar year filers, all income is considered earned on 12/31/xx and not ratable throughout the year, nor tied to quarterly (or other scheduled) distributions.
From IL K-1 Instructions:
When is pass-through entity income earned?
Pass-through entity income is considered earned on the last day of the pass-through entity’s taxable year. Pass-through entity income is not considered received equally throughout the year. The pass-through entity’s tax year ending date is listed in the upper right corner of the Schedule K-1-P you received.
As far as capital gains and other investment income, I'd turn to the consolidated 1099 which lists all of the stock sales. It should also list the dates of when interest, dividends, and capital gain distributions were actually paid. You can be the auditor is going to want to see that info, so you may as well be prepared.