Just remember any career your founder does, if he reaches level 10 - that career is no longer available for another heir/immortal's career requirement. Which is why if the time machine changes your career to that of another immortal's career at level 10, you can fail if they've both already eaten ambrosia.
Can the time machine change careers to/from Self Employed Careers, or just rabbit hole careers? I thought it was the rabbit hole careers that could be changed by the time machine, and only to other rabbit hole careers. At least that's what happened to me, my founder in the Province Dynasty Supermaxed Cooking Skill and Maxed the Cooking Career and then through the time machine travels of one of his sons, he changed to being top of the medical career (which is one I've never maxed personally/intentionally before)
I was going to have each Immortal max a self employed career as their unique maxed career (I worked out there were at least eight options) and then change them to a rabbit hole career to keep them out of my hair.
My understanding was that one could get the following as Self Employed Career options if one has all the expansion packs (which I do have):
Writing
Painting
Gardening
Fishing
Sculpting
Inventing
Photography
Alchemy
Nectar Making
Riding
Mixology
I've had the least experience with Mixology, Riding, Nectar Making, Alchemy and Photography, however.
My founder did Sculpting and Gen 2 will do painting when he/she is born.
With Photography, I plan to have the person with that as a career supermax another, easier skill to supermax, possibly cooking or charisma (to me, charisma seems to go hand in hand to some extent with photography, and I do find it kind of easy to supermax). Charisma is of most interest to me as it seems that it is less likely to be 'accidentally' mastered by someone else.