Checking the rules for the petrified condition, Enlarge Person and for transmutation spells in general shows that there is nothing that mutually excludes both effects at once. Specifically, a petrified humanoid does not change type and become an "object" - it is still the creature, but with a condition applied.

There is no apparent "freezing" of ongoing effects, spell durations etc, which should really be noted under the condition if that was the case. There may even be undesirable exploits to make cheap permanent effects tied to petrified creatures under otherwise temporary effects.

So in my opinion, that supports your option 2:

(2) The petrification creates a statue of one's current form, but when the spell wears off the new stone statue changes shape.

However, I think there is ample room for DM interpretation supporting either of the other two options, and even variations depending on what kind of effects can be "frozen in" when a character is petrified. It would be a minor ruling either way, and only require a little consistency during the game.

A side-effect of supporting option 2, is that if you cast any visible effect that does not affect normal objects on apparent statues, then you will see which ones are in fact petrified creatures from how the spell works (or not). As there is no competing "detect petrification" spell as far as I know, I think that is probably ok.

According to the traditional summoner's eidolon class feature, this isn't a problem unless the GM says it is...

The traditional Pathfinder summoner's eidolon class feature says that

A summoner begins play with the ability to summon to his side a powerful outsider called an eidolon. The eidolon forms a link with the summoner, who, forever after, summons an aspect of the same creature.... Eidolons are treated as summoned creatures.... A summoner can summon his eidolon in a ritual that takes 1 minute to perform.... The eidolon remains until dismissed by the summoner (a standard action). If the eidolon is sent back to its home plane due to death, it cannot be summoned again until the following day. The eidolon cannot be sent back to its home plane by means of dispel magic, but spells such as dismissal and banishment work normally. If the summoner is unconscious, asleep, or killed, his eidolon is immediately banished.

Emphasis mine. The term eidolon is used for two distinctly different creatures in this description. First, the eidolon is the creature to whom the summoner forms the link. Second, an eidolon is a summoned aspect of the creature to whom the summoner formed the link. The first, the linked eidolon, is unalterable without GM intervention. The second, an eidolon aspect, is just an incredibly complex creature that's summoned.

The description of the Conjuration school explains the significant differences between a creature that's summoned and a creature that's called. When a creature is summoned, the effect

brings a creature... to a place you designate. When the spell ends or is dispelled, a summoned creature is instantly sent back to where it came from.... A summoned creature also goes away if it is killed or if its hit points drop to 0 or lower, but it is not really dead.

Emphasis mine. A summoned eidolon whose summoning effect ends returns to where it came from. However, the DM may have confused a summoned eidolon with a creature that's called. When a creature is called, the effect

transports a creature from another plane to the plane you are on. The spell grants the creature the one-time ability to return to its plane of origin, although the spell may limit the circumstances under which this is possible. Creatures who are called actually die when they are killed; they do not disappear and reform.... The duration of a calling spell is instantaneous, which means that the called creature can't be dispelled.

This means, for example, a called eidolon would die only once ever, but a summoned eidolon can be summoned over and over despite its apparent death, banishment, disappearance, imprisonment, or whatever. The eidolon aspect is summoned not called.

Thus the summoner should be able to take a standard action to dismiss an eidolon aspect then summon again an eidolon aspect when he's able even if an eidolon aspect is 100 years in the future because the link the summoner formed is not to an eidolon aspect but to the linked eidolon from which the summoner summons an eidolon aspect. Even if an eidolon aspect is 100 years in the future, the linked eidolon should still exist during the summoner's time unless the GM's messed with that, too.

A clumsier, more succinct argument along similar lines in fewer words

As a summoned creature, an eidolon is instantly sent back where it came from when it's dismissed, killed, or whatever, and an eidolon transported 100 years into the future didn't come from 100 years in the future but 100 years in the past.

...Yet the GM may say the eidolon's disappearance is still a problem

I can't have all the information about the campaign, but it sounds like the summoner might've run afoul of the DM. It's easy to do with a summoner, which is widely considered one of the game's most powerful classes.¹ It's possible that the DM decided to take away the eidolon only briefly—like some DMs are wont to do with a wizard's spellbook—because the DM assumed he occasionally should despite the game making eidolon removal really difficult (e.g. maybe an instantaneous effect like petrified persists until the effect can be removed). By pointing out the rules, the DM might, instead, take more drastic measures to mitigate the character's power.² Alternatively, the DM could be planning something awesome but is unaware of how the eidolon works and citing the rules sabotages what might otherwise be a really cool plot.

So before you bring this up, talk to the GM about his plans and confirm that he recognizes how much of your character is bundled into this creature your character summons. If the GM appears sympathetic and says that you should wait a couple of sessions and everything'll be fine, then be patient. If the GM cackles maniacally and says that you're screwed, then bring up the rules.

Time travel yourself: A last resort

If it looks like the GM will never return your eidolon—despite this answer—, and you're nothing without an eidolon, and you've nothing tying yourself to the current time, wait the 100 years. Many possibilities for time traveling the hard way exist—most of them inconceivably boring—, but probably the most painless is to master a homunculus; buy stone salve and a scroll of flesh to stone; find a safe place to hole up (e.g. an elven law firm, a dwarven bank, an ancient creature's heavily-traveled and treasure-filled lair);³ order the homunculus to rub the stone salve on you in 100 years; and cast flesh to stone on yourself, voluntarily failing the saving throw. (The homunculus will be fine—it only goes nuts when you die not when you're petrified.)

However, expect any plan like this to go horribly wrong.

¹ The summoner seems powerful because most choices are good choices. The summoner still pales before full casters. (Although some do call the summoner a full caster in 2/3 clothing because of the way its spell list is organized.)
² The most extreme measure being killing the summoner, obviously.
³ Okay, not that last one.