How to verify the runway numbers in a systematic way given the high workload during landing?
There are a few common (?) techniques you could use, although how you work them into your actual checklists is up to you. Here are some that I've been taught, there are probably more:

Tune the localizer and/or load an approach

Pros: reliable and accurate (if you set the avionics up right) because it gives you guidance for a specific runway
Cons: can lead to fixation on instruments when you should be looking outside; not every runway has an approach; your aircraft may not have the necessary avionics; may be awkward or distracting to set up and verify

Set the heading bug to runway heading

Pros: many pilots do this for takeoff, so it's a familiar check; works for any runway; convenient if you go around and are told to "fly runway heading"
Cons: doesn't uniquely identify a parallel runway

Write the runway number on your kneeboard

Pros: simple; easy to glance down at quickly
Cons: none that I can think of, unless you don't have a kneeboard

Or use all three techniques together, of course.

ATC could still change your landing clearance, or something else could force a change of plan, but stuff happens and you just have to deal with it. Personally I like the localizer/approach method at night and/or at an unfamiliar airport, otherwise I'll just write down the runway number on my kneeboard.