I would say it is fairly common to blow breakers or gfci's on medium to larger jobs, especially incan. As of this year, we are finally moving towards LED mini lights. But no on c9's. Set a policy in your business that as current mini lights wear out, or new ones installed, they are only LED or you don't do it. Try to take some of the money you make now and troll the internet for LED mini's you can stockpile for next year. I always seem to be broke the first few weeks of the season, so buying them now makes them appear "free" next near. This customer may be lost to you, but if not, you have to draw the line somewhere, and I think all new LED lights coming in in the future is a good start.
As to the customer specifically, when I bid jobs, if I go over a certain amount of c9's or mini's, I am looking at their power meter to see if they have an available circuit space in that box, or the breaker panel space, and I include $200-250 to pay my electrician to have a double outlet double breaker installed. I tell the customer in the bid it includes it, but I usually don't line item it. If you do, the customer will think they have the option of coming up with a free solution, which is what has happened in your case. I have a 2 gang box with bubble cover, 20 amp plugs installed on the a/c compressor outside box on each hot run. It is marked seasonal lights only, as it cannot be used during off season when the A/C is running. we pay about 150 for the outlet and then another extra $50-$100 or so for a few 100's or 50' cords to get the power over the roof to the good outlet. The A/C option may not work south of here where they run the A/c at night after November 20 or so. Here, on heat pumps you cannot tap in, so we find a bedroom outlet on an outside wall and drill through, even if it is on a top floor. dining room or living room outlets also sometimes work, but staye away from drilling from kitchen, bathroom or garage outlets. those tend to be maxed out by a toaster, hairdryer, or garages fridge.
And I know what you are thinking...I ain't paying for her outlet. truth is, you already have. probably 3 times over. in the extra time to fix stuff and run crazy cords everywhere and try to reroute and figure out how many amps you can put where ever.
I was in the same boat with two clients this year, partially my fault. I added fairly extensive landscape lighting to two larger clients and this season they really needed power for large Christmas displays. one was easy, we did an a/c double outlet and took care of it.
The other was more extensive, a $750 or so upgrade, we had a Heavy duty 40 amp 240v timer installed that runs a new subpanel with 6 20 amp breakers and 6 outlets. roughly 80 amps of capacity on the 120v side. so more and longer cords, yes, but no more seperate timers, and no more extensive instructions to employees that you can only plug in 5 amps, here, 11 amps, there, etc.
It SAVED almost 6 man hours on the install, and she is thrilled with all of it coming on and off at one time. In future installs, any jobs over 6k will automatically get a version of this system. having one power point and one timer is just too easy.
Sorry you are in this situation, but the best thing to do is to learn from this and move on, and change how you deal with all future customers. always include the cost of the outlet in medium to larger bids. and don't budge on it.