Yet another reason blocking ads is a must. But not just blocking ads, trackers as well. I use uMatrix and uBlock origin. Unfortunately this does nothing to deal with the aforementioned redirect chain. I suppose maybe this means it is time to go back to the telephone and flight agencies.
Some of the tracking protection tools might help, but not all for exactly the reasons you mentioned.
However, you can enforce some settings in Firefox and Firefox based browsers to control referrer leakage in control. But it does break few websites. I can recommend taking a look at : https://wiki.mozilla.org/Security/Referrer and see what suits your need.
I wonder if enabling referrer trimming by default on common browsers would force people willing to use tracking to reconsider their practices. Like everything (it seems) it is always a game of cat and mouse, and the best way to make it harder for trackers is to make sure the targets keep moving.
>> I suppose maybe this means it is time to go back to the telephone and flight agencies.
You would just end up paying more (directly or indirectly) while still having the representatives using the same problematic system, now from their end.
There is really no way out of the redirect chain here, but if you want to avoid malicious redirects on many other websites you can use the Neat URL extension.