I understand the budget and time constraints. I haven't had to deal with the amount of buildup that your engine has but I do have a suggested procedure you can try.
1) Start by putting the old pump back on for the cleaning process. There is no reason to expose the new pump to any chemicals.
2) Plug all the oil passageway holes with corks or stoppers (the home center should have them). You don't want to get any chemicals down in the oil.
3) Take liberal finger loads of grease or Vaseline and build a bead/dam between the bores and the tops of the pistons. As above, you don't want to get chemicals in places they shouldn't be. Coat the walls of the bores with grease/Vaseline while you're there.
4) Hose out as much of the block as you can to dislodge crud. Consider feeding the water to the bottom radiator hose so the water flows up through the block and out. You'll see why I suggested to coat the bores and pistons with Vaseline. This will be messy.
5) Let all that water drain back down and out.
6) Go to Advance Auto and look for a bottle of green liquid called "Right Stuff Rust Remover". Sometimes home centers have this or a similar product. You're looking for a de-ruster with phosphoric acid.
7) Use drill bits (by hand) to open up the water passageways as much as possible.
8) Plug the open lower radiator hose and use a funnel to fill the block up with the phosphoric acid. Fill it all the way to the top of the block.
9) Allow the chemicals to work overnight, then try using some gun cleaning brushes as mentioned above to clean out the holes as much as possible. Top the block up again with phosphoric acid and wait another day, then repeat the gun cleaning brushes.
10) Flush the block (bottom up again) with fresh water. Let the water run for a while to get all the acid out.
11) Finally... put the good pump back on. If you need a new gasket, check your local parts supplier to see if they have one for a '74 MG Midget. If not, buy gasket paper and cut your own. Do not re-use the old gasket.
12) Look at your picture above. Do NOT put that accordion hose between the head and the new water pump. Replace it with a piece of 1/2" heater hose (or is it 5/8"? I forget). The only reason those accordion hoses exist is for emergency repairs. They are weak and should not be placed back on a car when the head or water pump have been removed. Standard heater hose cut to length will work much better.
13) Clean up everything REALLY well. Remove all the plugs and Vaseline and put the head back on.
You can see this is a lot of work. Fitting a donor engine would in fact be quicker (if you had one, and if you had the money and time).
Footnote: The CLR mentioned above is a version of phosphoric acid. It's weaker than the product I'm suggesting you get but CLR or Lime Away will work (somewhat) if you can't get the products I suggested. Do not be overly alarmed at using phosphoric acid. You drink it every time you have a Coke. It is an acid so normal caution is advised (eye protection, etc), but it's relatively mild (unless you're rust) and it will break down naturally without causing a lot of environmental damage.
I'm sure my method above is TMI, but given your constraints, I'd try chemical cleaning in place.
EDIT: ALSO, cover the distributor with plastic grocery bags before all this wet work. Make sure you keep it dry to avoid problems when it's time to restart.
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