I think your proposal sounds good, you already have most of the parts you need.
Regarding the chainset, Chris Bell on his website suggests that up to 10-speed there is no real difference in ring spacing or if there is it should be minimal.
There is often confusion about so-called '10 speed chainrings' and '11 speed chainrings'- but there are no such things ...
When removing a bottom bracket, since the available surface is so narrow, it helps to use a proper bottom bracket tool.
Measure the distance between opposite flat sides and then search for "bottom bracket wrench" + (size), e.g. https://www.google.com/search?q=bottom+bracket+wrench+36mm
They generally look something like this:
I suggest you stop using a spanner. That way leads to damaged parts, damaged knuckles, and tears.
Instead, get a socket of the correct size, and a ratchet bar to turn it.
Finally, have a good look at the visible threads and make sure you're turning it the right way, which will be the same turning direction used to remove the locknut.
You can do this, just ...