You say it's BSA and that it's DS LH, NDS RH thread, but you don't corroborate what exactly the thread size is. It will be easier to get to a good result here if you know what the thread is. It's easier with a thread pitch gauge and caliper, but perfectly doable to the extent needed here (ie telling the difference between 24 and 26tpi) with a ruler.
As has been pointed out in the comments, the first question is whether it's a Raleigh thread (26tpi instead of 24). You should really measure to get that sorted out.
If it had FC-1050 in it before you can't assume the BB was BB-1050 or any other particular BB. BB-1050 has its model name and thread stamped very clearly on it so unless it's long gone or something, it sounds like they may not be what it was. Meanwhile, as in the Sheldon link, re-using the cups and transplanting in a JIS spindle is a very good way of addressing BB/crank type repairs on Raleigh shell bikes, so it's plausible that was done at some point.
If it's a 70mm, 34.8mm x 26tpi Raleigh shell and the goal is to install 24mm Shimano road cranks, the main question is whether you're up for first confirming the cranks you want will clear the rest of the frame once you make the necessary modifications to run them, then grinding/filing and refacing the shell down to 68, then acquiring the Phil Wood 26tpi cups to do it.
If it's 70mm, 34.8 x 26tpi Raleigh and you don't want to jump through those hoops, then keeping it square taper is the clear choice. If you want to make it cartridge you can use the Phil cups and BB for that. If it needs to be a lower end repair, serviceable Raleigh cups are not scarce in the world, as Sheldon pointed out, but they'll need to be acquired used/vintage.
If somehow it is 34.8mm x 24tpi but has a 70mm shell width, that makes it a random oddball. The main consideration becomes that external road cranks with ISO/BSA BBs generally speaking don't just have 2 extra millimeters of space to give like that. The spindle won't be fully engaged into the left crank on a Shimano road crank, for example, which may seem to be fine in the stand but isn't necessarily safe. Depending on the crank, you can also have issues with the bearings not contacting the proper machined areas of the spindle, causing play or creaking. Italian external BBs use thinner cups to get to the same face-to-face dimension, but that doesn't help you. The straightforward thing to do again would be check the clearances, file the shell down to 68, and face it. If that was an unattainable solution, the only thing I can think of that allows you to put new cranks on and have everything be arguable as technically "right" is just use a Phil square taper BB, which are uniquely oblivious to the exact shell width because they can be inset on both sides. Alternatively, again if that's all too fancy, you could run a normal 73mm cartridge, put a 1.5mm spacer on the DS, and see how it does being down 1.5mm of thread engagement per side on the cups. (You would find a square taper road crank and use whatever spindle length would normally be called for with your chainline needs, only you'd be getting the 73mm shell version).
