If the bloomjbikes is interested, I have a pair of shimano 7speed trigger shifters with indicators that I'd offer to the project for the cost of shipping. Not the prettiest but would work and minimize the cash outlay. I think this is the biggest challenge of the upgrade…

After looking at the pics, I'd keep the crank (used one on another bike I fixed up earlier this year), replace the chain, cassette, and derailleurs along with brake pads. A lighter tire on the original wheelset will greatly change the way the bike rides too.

What about the following items:
Shimano M360 rear
Shimano M310 dual pull front
Shimano HG41 cassette
Shimano HG40 or SRAM PC-830 chain

if t were mine I’d do a vbrake upgrade. I’d donate brake handles that work with canti and vbrakes to the cause with the shifters.