It was my intention to complete this immortal dynasty with only the base-game installed. If I were to compromise my intention, would I be able to install an expansion to have more LTRs available to finish and still be eligible for Hall Of Fame? My last immortal is a baby so I am rather close to finishing.
I saw no one addressed this yet, and I'm not sure if it's still a consideration, but...
The general rule re expansion packs is, "install upon initial acquisition, or play without." In other words, you could only install additional expansions when you first purchased them (since they were new to you), but if you opted to not do so, then you were stuck without them for the duration.
However, the final call is, as always, Metro's.
(I counted
here that there are 30 base game LTR, and by removing the Midlife Crisis, that gives you 29 - you would need only 24 unique ones, and have 5 overlappings. Is there not even the uselessly frivolous one or two you can use?)