The quickest but not cheapest way to make it faster is to get a water fed pole. Short of that it is a combination of technique, routine, and efficient tools that limit detailing.
If you can get away from using a ladder, that is going to save you a significant amount of time. The best way for this is to use a WFP. The next best thing would be a traditional pole with a swivel squeegee and mop. You would need to have a very practiced technique to make this efficient but I have used an 18" Moerman Liquidator channel with the Fliq pad applicator to do second story windows after the initial cleaning. Barring those two options you are going to have to hustle with the ladder.
On most of my residential windows I use an 18" mop and 18" Liquidator squeegee all the time. I have literally zero detailing on 90% of my windows. Some frame designs don’t keep the squeegee from sliding off the pane and there is sometimes a need for a quick wipe along one edge, but for the most part I save about 45 minutes of towel detailing by using this tool. Also, having a practiced hand position and angle on the rubber helps to keep the water collected in front of the blade and limit movement with the squeegee which also saves time. I usually start in the bottom left corner of the glass with the squeegee upside down. I pull straight up and pivot the outer edge along the top portion of the glass pane. Now the outer edge is in the top right corner and I have the option of a straight pull down to the bottom leaving a slight angle with the inside portion of the squeegee higher so that I can slide it back to the left corner before closing out. This is a basic 4 movement box technique. It only works if I have been able to collect all of the water as I have moved along, otherwise I start out the same until I am in the top right corner with the squeegee oriented down and I bring the squeegee straight down halfway before angling the inside edge upward and dragging it back to the top left corner, pivot do a straight pull down to the bottom left, pivot again and drag the blade from left to right finishing in the bottom right corner with the squeegee oriented vertically. I think this is referred to as the Z technique, just a variation on where you start your squeegee.
Reduced movement of your squeegee fanning technique will save time removing water from the glass as well as detailing especially compared to straight pulls.
Using a new “sharp” squeegee rubber is also going to make things more efficient and less likely to leave streaks that you have to go back and detail. I think someone once put it as: “It is easier to replace a $3 rubber than it is to save $3 worth of time while wiping windows.” Even if you changed your rubber everyday, which is insane for residential cleanings, having that sharp edge will help you make more than that by saving you time detailing.
Routine wise, I always work from the top down, I go inside and remove all the screens first. In my case, with second floor screens, I spin them like a frisbee as long as there are no obstructions below. This spin allows the screen to catch the air beneath it and gently float to the ground without doing any damage to the screen or frame. It also keeps me from carrying the screens through the house and dropping mold, mildew, or dead reptile carcasses inside the home. Retrieve the second floor screens separately from the first floor screens in the same rotation around the house so they are in the right order. I pick a point to start and stop at and work in a single direction. Clean the screens and set the aside to dry. (I use my pressure washer to clean the screens, but only because I have a trailer mounted system with a water tank so there is no set up for me to get started. I turn on the pump, spray the screens with my bleach based detergent to kill any mold, mildew, or algea, then I rinse the screens with my pressure washer using high volume and very low pressure. No hand scrubbing, no wiping, no damage.)
Depending on what time of day you are starting, try to start with the glass that is already in full sun and work your way into the shade. In the morning you would start on the East side of the house then South, West, finishing on the North side. In the afternoon, start on the South side, then West, North, and finish on the East wall. This will help keep you cool while working and finishing in the shade allows you to take a few minutes break out of the sun if it is a real problem like it is here in Florida. I do not lug a bucket around the house with me, I have my squeegee soaked and in my hip bucket. So by starting on the glass that is the hottest, I have enough water in my mop to allow me to clean and squeegee before it evaporates off. If your mop is barely wet, you will find that the little water that is applied to the glass will dry off before you have had a chance to squeegee it off and you will have to start all over again. I use the Moerman microfiber mop and it is usually good for 15-20 average double hung windows. But a quick walk back to my bucket and a dunk gets me back in business for any remaining windows. By the time the outside is done, the screens should be dry and you can go inside and start on the second floor, clean the glass, wipe the track/sill, and replace the screen. If you follow the same direction, you should already have your screens in the proper order for placement.
The county I work and live in does not allow you to operate any mechanical equipment in residential areas before 8 am or after 8 pm or dusk in the winter which is as early as 4:30 pm. That being said, I have worked in the summer until 9 pm to finish a the window cleaning portion of my day at a house as long as there is still enough light for me to see if I am leaving any streaks behind on the glass. It is up to the client to determine what is too late or too early, you are the one in their space. I had one really long day at a client’s house where they made me a plate for dinner I was there so long with all the things they wanted to have done.
Wow that was a lot.