Is this a scenario where 1.2.3.4 represents the production website, and 5.6.7.8
is the same website, but for example in a new version, but which has not been
deployed yet to 1.2.3.4  and is therefore only accessible so far on 5.6.7.8?
And you want to create an offline copy of it before relaunch?
Assuming the new version of the website appears on <http://5.6.7.8/>, did you
try to do just simply then:

httrack <http://5.6.7.8/>

?