Interesting little exercise, glad you said you weren't worried about efficiency because that is going out the window.
Let's set the playing field, what you want to end up with is where you start from so:-
Target (for discussion) is 22.5 (5 Imp Gal) of 1.050 wort in the fermenter, made up of 12.5 L of wort and 10 L of "sanitary" ice. "insert raised eyebrow emoticon here"
Shuffling some numbers around, 1.050 wort is (roughly) 12.5oP, or 12.5% w/v extract, we need the same amount of extract in 12.5L of heavy wort, (22.5*12.5/100)=2.8125 Kg of extract.
That means the heavy wort is going to have to be (2.8125/12.5 * 1000)=22.5oP or from (SG= (oP*4)/1000 +1)=1.090. that's doable, expensive, but you can get up over 1.100 if you really try.
Heavy worts throw proportionally more trub, so let's budget for leaving a good 2L in the kettle so we need 14.5L of 1.090 wort at the end of the boil.
Let's call your evaporation an average 10%, so into the kettle you need just a touch over 16L, that contains all the extract so your running's need to have a gravity of 1.081 or 20.25oP (same dance as above) to give the required 3.2625 kg of extract. Remember the 2L loss has the same gravity as the cast wort.
Just so happens that the "first running's" form a mash made at 3:1 will be very close to 20oP, (I'm going to be very lazy here and just use some quick rules of thumb because this far out near the edge of the brewing universe there is going to be a fair amount of guess and be dammed)
If you mash at 3:1, you get roughly 2 back and the grain keeps 1 (nearly)
You want 16L of heavy wort times (3/2) is 24L mash in and 8 Kg of malt (if you have no dead space in your tun).
Something like 55% brewhouse yield, doing rough numbers with just a good Aussie Ale malt with a potential yield of 75%
Naturally you are nearly leaving a beer behind; you might want to read up on "parti-gyle" and knock out a Mild with the leftovers.
Have fun
MHB