My vote's for circular saw, largely on the basis that for some reason my ability to cut in straight lines is an order of magnitude better[1] with them than it is with most of the obvious alternatives.
The clamping something to keep the cut straight advice would seem to be key, regardless of what tool you use.
[1] I'm suspicious that I may be channelling raw FEAR into steady-handedness.
I'd happily agree with you.
But, having recently had to perform said task and A) not being in possession of a circ saw and B) being unlikely to subsequently need one anytime soon ^ that was my solution (which, I'm happy to say, worked).
More of a concern for me was the the removal of the slotted brass screws, by which the door was hung, in 1930-something, covered with about 30 coats of gloss paint, without damaging them to the point at which they cannot be removed. Thus making the job an exponentially major pain.
However, I'm delighted to report that an impact driver, driven by a FB hammer rendered the task a surprisingly easy one.
The door went back in using steel Spax Pozidrive twin spiralled screws.
The brass ones went in the rin-tin-tin.
Mother is happy, her door closes over her new hall carpet, without making crop semi-circles in it.
My work here is done.
