Should I notch the bearer to fit the joists

Veranda replacement on an old Queenslander

Pre-existing timbers I plan to replace are as follows:
Bearers 120x75mm, span approximately 2250mm (note joists are notched into the bears about 20mm), I assume this was to provide fall on the deck, note sure it may have even had T&G boards on it once upon a time.
Joists 100x50mm, span 2250mm

Replacement timbers
Joists F14 or F17 100x50mm. I think I have this one worked out.
This meets the span tables (Allan Staines single span 2200 for F14 and 2400 for F17) I only have 100mm to squeeze it into the existing gap between the bearer on the other side and the floor of the house). Joist spacing should come in at about 400 centres, currently the joist spacing ranges from 540, to 460. I don’t think the springy feeling under foot with 19mm decking on top. Add to that the current design has decking counter levered 260mm against one wall with no joist under it right where you walk up the stairs and into the house.

Bearers
I only need replace the ones at front of the veranda the other bearer is pre-existing and is now supported with steel stumps and a load bearing wall with posts at 450 centres)
The load width is 1100, tables provided by Staines for a load width of 1800 are as follows
Single Span of 1800 F17 100x75
Single Span of 2100 F17 125x75mm or 150x50mm
Single Span of 2400 F17 2/125x50
Single Span of 2700 F17 150x75
I would really like to still notch the joists into the bearers. I am not a big fan of joist hangers, plus the underside of the decking is visible from the patio underneath. I just don’t think the deck hangers will look original. Plus I assume this would require going up in bearer size to get the required height, as I am not moving the 350mm stumps which have been replaced recently.

THE PROBLEM
If I choose bearers such size such as F17 175x50, this would mean I would need to notch the joist by 75 mm to give the same fall that the deck currently has. In effect leaving only a bearer of 100x75 (which is in effect what is there now a 120x75mm notched 20mm =100x75). I assume the strength of the notched bearer would only be as strong as the non notched part of the timber member. This leaves me with a 100x75mm bearer which is only suitable to span 1800.

To add to problem one bearer will also be supporting the stairs, although one stringer will sit on a house stump the other stringer will need to be supported by the bearer.
Before I decided to replace the bearers and joist, I ordered some hardwood timber for the facia board. I was planning on bolting the facia to the bearers to strengthen them. The facia is F14 190x32 DAR.

If I rest the facia board on the stumps and bolt it to the bearers with M12 would this be sufficient to strengthen the bearer.


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