Edit: please assume in this scenario the Grand Tribunal ruled immortal magi are protected by the Code soon after their existence became an established fact.
My great interest for immortal magi as a viable option for powerful and experienced characters and a recognized (if not so common) existence within the OoH led me to consider various topics.
Would other magi demand a political check to their influence in the Order? Or would they be too rare and/or reclusive for the issue to matter? If the latter, a possible compromise would be to limit their voting rights. Other mages expect and assume immortals to have gone into retirement and abstain from Order politics in normal circumstances. They hand over their voting sigils to trusted proxies, much like retired magi in the Rhine Tribunal. Their status as Hermetic magi in good standing is recognized and their rights protected. They can take part and vote in a Tribunal if they are involved in a case or the Tribunal faces an emergency. This issue does assume other mages can easily recognize the value of letting immortals keep their rights in exchange for the insights they can provide and potentially pursuing immortality themselves.
There are various gainful synergies between immortality methods and other kinds of magic. (Durable) External Soul and the Great Elixir seems one of the best ones, since the former can protect alchemical immortals from destruction and the latter makes them immune to Twilight. Mystagogues that are interested in this issue should track down some Gruagach or better Koldun, persuade or force them to share the script, and adapt it to their Cult Lore. An even better course would be to enchant various protective effects on the stone, esp. if the Durable option is not available. Unlike Gruagach or Koldun, Hermetic mages face no serious limitation on this.
The combination of Living Ghost and living corpse seems another excellent one, since it would greatly increase the immortal's resistance to banishment or exorcism, as well as remove their time limit to stay away from the Haunt. Another good idea would be to have enchanted objects for instant travel to the Haunt in emergency situations. An even better solution would be to integrate Canaanite Magic, since it provides a permanent link to the living world that replaces the need for a Haunt or possessing a body. I am not sure if (Durable) External Soul can do anything worthwhile for Living Ghosts.
One of the most important and likely reasons for magi to pursue immortality is to gain unlimited time for research. TMRE covers the issue of immortal mages retaining knowledge of Arts/Abilities and spells by talisman enchantment, but magi can pursue other kinds of valuable knowledge, such as breakthrough insights and initiation scripts. I am tentatively assuming immortals can retain insights by the same method, at a conversion rate of 1 Xp = 1 Insight point.
As it concerns scripts, I tend to assume the Initiation experience itself (including working as a Mystagogue) would automatically imprint knowledge of the script in the immortal by mystical means, since initiation works the usual way for immortals to change relevant aspects of their nature. The only meaningful difference is they cannot use Ordeals (but they have unlimited time to pursue a lot of Quests, so it balances out). If the mage later changes the script they automatically retain it if they use it for themselves or others before it fades from memory. Otherwise they may need to enchant the knowledge in the talisman. A script broadly resembles a spell, but I am not sure about the conversion rate, since it has no level. Tentatively, you might deem it the equivalent of 1 Xp.
Of course, an alternative way for immortals to retain knowledge is to consume vis.