Fitting stairs to joist

[ChrisZx]

My second (and hopefully final) staircase question, now with added newels after my last question.

Looking to have this staircase up to our loft conversion, fitted over our existing ground floor stairs:

This is how it relates roughly to the existing first floor joists and stairs opening in red (ie the joists below it, note this picture has missing newels/balustrades):

My question is about how to fix the newels - I assume all freestanding newels should be notched over a joist for strength?

• Newel 3 and 4 are between/next to joists so I can add noggins if needed so that they can be notched over some joist, fine
• Newel 2 is against a wall, bit of a funny layout as the wall is stepped (hence the extra balustrade) but I've no real concerns here, either fixings into the wall or build a small stud wall to make the wall flat and fix the newel and back winder stringer to that (manufacturers have recommendations for how the stud wall should be constructed)
• My problem is with newel 1. As a single newel it ends up 10-20mm away from the joist. I can't make the stairs wider as the newel wouldn't line up with the existing top newel on the ground floor stairs (need a balustrade in between them). I can't move the joist inwards as it will foul the ground floor stairs balustrade

So I thought about making newel 1 a double newel, as shown in green in the second picture. That would turn a 10-20mm gap into a 70-80mm notch, and still work for a landing balustrade. Would that be considered strong enough? I can't really see why not, but I'm not sure what is considered 'normal' and what isn't.

Also, I know it's normal to double up top trimmers, should bottom joists be beefed up as well? Is there any guidance on what should be done/what sizes are considered big enough? The full parallel joist and trimmer are 65 wide, cut joists 50, all 200 deep. Full joist has a span of 3m.

Thanks!