12 to 15 isn't enough, I'm guessing you are pricing OK, as that equates to about £10 to £12 a house which is about the same as me. I don't know your location but up north that's decent, maybe you could get more than that I don't know...
But I have done 11 just this morning (and have stopped for a bacon butty) I will cruise to 20 jobs today and probably finish between 2/3.
It sounds like you don't have much money to throw at this other wise why not just invest heavily in the lead generation if it's working?
If you have little money to invest then you need to canvass, leaflet or advertise for free on the likes of Facebook, next door etc. Maybe learn how to make a website and seo and get it ranking etc.
You either need to invest time or money you can't do nothing and expect anything to change.
In hindsight you shouldn't have bought that round at £5 a pop but what's done is done.
If you are limited to 3 days and they are full the only thing you can do is find new work at proper prices and drop the lowest priced ones as you go, before you drop them give them the option to remain on at £10 a house (but doubling their prices will be unlikely to go down well but worth a punt if you are going to drop them anyway)
The doesn't happen overnight, when started out I could only do 10 a day because I was slower and work was more spread out but with continuous advertising dropping and replacing customers I've now got to the point where 20 plus a day is the norm and I'm not working much harder for it.