@Scott1598 Forgive me if my comment comes off as rude, but here goes.
Your cleaning team has asked you for a very simple thing - a table with arrival and departure dates updated and resent by you for each new booking. My cleaning team(s) ask for the same thing, along with the number of persons, children and pets. As the host and the person who is benefitting from the property rental, I have no issues with updating and resending the booking table with each new booking. That is MY JOB.
Use the .csv file that is generated by going into your reservations*, choosing upcoming and then export the info to an excel file. The booking start and end dates are in this .csv. Strip the file of unnecessary data and then email it to your housekeeping team. I do this once a week.
*If you have reservations coming from a different source, you will have to add them manually to this table unless that source also offers a similar spreadsheet where you can import the data from one spreadsheet to the other, re-align it, re-sort it and send.