Well, you need to get your own mill. That will improve efficiency in a big way.
I have about the same setup as yours, and I sparge through a colander same as you do. My main kettle is 17L and I likewise have a 9L kettle for sparging. But then I also use other kitchen kettles and pots to make up the extra volume. I have brewed up to 6 gallons of beer on my kitchen stove, multiple times. So I have not needed to do a concentrated boil or dilute. Here is one example from a few years ago. Just do a partial boil in each pot.
So I still think you can try different things to work out a solution that can work for your homebrewery. Cheers.
I am having my brewday this weekend and I am considering trying this. I feel like there is not much gain for me, since my recipe calls for a 90 minute boil so I think that ~6L will be lost during boiling evaporation by each kettle that boils! I am going to explain what I have in mind and if you spot anything odd feel free to mention it:
To remind you, I have a 17L kettle as well as a 9L one. I also have a smaller one (I believe it is 4-5L) which I haven't used so far.
Also, I am huge fan of putting my main kettle in the oven in order to maintain its mash temperature.
So, what I think I will try is:
1. I will fill up my main kettle with as much water I can in order to be able to accommodate the grain volume but at the same time being as closer to full as possible. Not sure how to achieve that though, but I will try the following: my recipe has 4.4kg of grain. The grain absorption should be ~3L. I think that I should say "4.4 - 3 = 1.4" and hope that this 1.4 represents the actual volume that the grain will need in order to get into the kettle (3L will be absorbed so this is not considered as taking up space in the kettle). Once the mash is done in the main kettle, I will raise the bag, and let it drain on a colander placed above the main kettle. As per later comments on this post, I will also squeeze the bag
2. I will fill up my 9L kettle with 4-5L and get it to 77 degrees Celsius. I will also do the same with my 3rd kettle (4-5L) and get it ready for future step. I will transfer the bag inside that 4-5L (hoping again that there will be enough room there) and let it sit in there for lets say 5 minutes (?) to absorb more water. After that I will return the grain on the colander on the main kettle and let it drain. As per later comments on this post, I will also squeeze the bag
3. Since my main kettle is 17L to the top, I am able to put 15.5L in there as so to have a safe boil (no boil overs). If that volume is not in there, I will add from my secondary, where the sparge happened.
4. I will move the colander with the grain on top of my secondary kettle and I will slowly pour water from my 3rd kettle on top of the bag. I will let it drain and at the same time I will (if needed) add some water in my 3rd kettle, in order to have ~2L. Once the bag is drained, I will squeeze it (still above my secondary kettle).
5. Lastly, I will put the bag in the 3rd kettle and let is sit there for aprox 5 mins (?). After that, a final drain and squeeze above that 3rd kettle and at that point, I believe that if the grain could talk would scream "mercy. spare me. enough, I gave you everything I had".
At that point, I am hoping to have ~15.5L in my main kettle, ~8L in my secondary kettle and ~2L in my 3rd kettle. If one of the volumes is lower on main or secondary kettle, I will fill it up with water of my 3rd kettle. There is no point on boiling my 3rd kettle, it does not have enough volume to maintain a 90 minute boil. So if all these happen, I will end up with ~10L in my main kettle and ~2L in my secondary.
I don't know if i said something wrong, but if not, is all of this worth if for 2L extra wort (from my secondary kettle)?