Changing Door Handles

I have very ugly white gainsborough "classic" knobs in my house on all the doors. They are fitted with even more horrible round tube latches.

I want to change all these to levers. I work in a Mitre 10 so bought home a lever set to test it out to see if I can just change the levers and use the same tube latch.
They don't fit. The pins on the handles don't fit into the holes on the tube latch. So this means I will need to use the tube latches that come with the lever sets.

Do the rectangular tube latches have to be "checked" in to the door frame or can I just screw them in and have them not be flush with the door?
My other issue is that if this is OK the round hole isn't big enough for the new latches to fit through, so I imagine I need to get a spade bit and make the hole bigger?

Might be just easier to get a handyman to do this. I have around 20 to do and am not keen on doing them myself, I think i'd bugger it up for sure if I need to check out the holes for the rectangular plate.

Hi wendlle
The new latches need to be checked into the door. To achieve the 60mm backset you need to get the latch flush with the door edge.
The hard part will be making the latch hole bigger.
The old latches were often 22mm and new latches are typically 25mm. The hard part is you can't just stick a bigger spade bit in the old hole as spade bits need solid material to keep them centred.
You either need a 25mm drill bit or make a jig and then use a 25mm hole saw.
Probably easier to get a carpenter to do it for you.

Thanks for the reply. When I went to work today I was thinking, why not just try to drill out the hole a bit that the new latch won't fit into. The issue was the two holes in the shaft of the tube latch were too small for the new handle "pins"
And voila, a slightly bigger drill bit than the hole did the trick. So I can now do this to all the tube latches and fit new levers with the existing fittings.