This is really strong, at least for certain builds. Anyone who wanted to focus on Str anyway is likely to end up playing this race.
Firstly, Barbarians. Barbarians are currently one of the most MAD classes in 5e, needing good Str, good Con, and at least reasonable Dex. Your race would allow them to dump Dex and just focus on Str and Con.
Secondly, Druids. This is probably the worst case - your proposed race gives a Moon Druid an incredible boost to their Wild Shape forms. Str and Con are the strong points, and AC is the weak point, of most beasts, especially the ones Druids like to Wild Shape into.
Next, Fighters. This is the least problematic, since a Fighter could already afford to focus solely on Str and Con, but it does mean they end up with a better AC than they otherwise would have.
Oddly enough, it also enables Str-based Monk and Rogue builds. This isn't really a problem though, since in many ways Dex is inherently stronger than Str anyway.
Comparing it to Monk isn't really that useful, since they're essentially the same, but anyway:
Level 1: Typical Monk has 16 Dex and 16 Wis, giving them an AC of 16. A Barbarian of your proposed race has 17 Con and 15 Str, giving them an AC of 15, or 17 with a shield.
Level 4: Typical Monk has 18 Dex and 16 Wis, giving them an AC of 17. A Barbarian of your proposed race has 18 Con and 16 Str, giving them an AC of 17, or 19 with a shield.
Level 8: Typical Monk has 20 Dex and 16 Wis, giving them an AC of 18. A Barbarian of your proposed race has 18 Con and 18 Str, giving them an AC of 18, or 20 with a shield.
Level 12: Typical Monk has 20 Dex and 18 Wis, giving them an AC of 19. A Barbarian of your proposed race has 18 Con and 20 Str, giving them an AC of 19, or 21 with a shield.
Level 16: Typical Monk has 20 Dex and 20 Wis, giving them an AC of 20. A Barbarian of your proposed race has 20 Con and 20 Str, giving them an AC of 20, or 22 with a shield.
Your proposed race can always have a better AC than a Monk of the same level if they choose, despite the inherent weakness of starting with +2 in a single stat rather than +1 in two stats.
You're right that basing it off Dex and Con would be even stronger, but only because Dex is inherently stronger than Str. Your footnote about bonuses, however, is less accurate. A minor bonus to AC, while good for everyone, is hardly a game-changer. Your proposed feature, on the other hand, can form the foundation of a build. It replaces a core feature of the Barbarian or Monk, and is effectively completely free, especially since your proposed race has fire resistance on top of it.
Feline agility and the potion of speed both apply.
The rationale stated in the question for these effects not combining is:
an effect that already doubles my speed is in effect
However, the question assumes it is fine for multiple effects to increase speed by 10' (fast movement, mobility, and longstrider). The interaction between feline agility and haste is no different -- they are two different effects. Just as the three speed-increasing effects combine to add a total of 30' to the character's speed, the two speed-doubling effects when applied together quadruple their speed.
The rule about duplicate effects is specific to spells (PHB, p.205, emphasis mine):
The effects of different spells add together while
the durations of those spells overlap. The effects of
the same spell cast multiple times don't combine, however. Instead, the most potent effect—such as the highest bonus—from those castings applies while their durations overlap.
For example, if two clerics cast bless on the same target, that character gains the spell’s benefit only once; he or she doesn’t get to roll two bonus dice.
There's no reason to think that spells interact with other game features any differently. There are numerous examples of game features applying similar bonuses to game statistics; that's the way the game works.
Best Answer
You are almost exactly correct.
All the math you have is accurate. However, you've missed a subtle rule mentioned in the PHB (pg. 202) regarding spells cast as Bonus Actions. Namely, when casting a spell as a bonus action
Thus, while it is possible to reach 27 AC using the methods you've described, you cannot cast Haste and Shield of Faith on a single turn.