Hi - we went thru a similar process & decided to separate our price + the cleaning fee. That seems to have been OK, especially because we always meet our guests and make a point of dropping “the young lady who cleans for us” or something like that into the welcome. We’ve had some guests leave an extra tip for her!
Also, some hosts put a 2 or 3 night minimum stay on their listing, especially during their busy season. (That means only 1 cleaning for multiple night’s income.)
And, we just had our taxes done & were able to itemize her pay, that of our gardener, the cost of the new washer/dryer set needed to do larger loads, detergent & cleaning supplies, etc. … it all adds up to reduce the costs of hosting.
I hope this helps!