I'm just behind you, just about to kill the Spectral Keeper, this is my... like 12th playthrough now, lol...
Your HP is a little too low, you should be looking to have Auron at around 5-6k by the final boss, right now my Auron has exactly 5032HP lol, and I've just broken off into Tidus' grid and nabbed some HP and strength.
Your other characters can obviously have lower than 5k HP, I mean, my Wakka and Kimhari have 4600 and 4800 respectively, Tidus has around 3600, Rikku has just over 3000, and Yuna and Lulu both have around 2800, and I'll still be levelling them up more as soon as I get the air ship back.
As other people have said, the best place to go is the Omega Ruins, you may struggle a little, but once you level up and can level there with ease, you'll find it's definitely one of the best places to do so, and your characters will be powered up in no time!
You should really look for a guide on how to get peoples celestial weapons (Their ultimate weapons) and how to power them up to their max potential... Celestial weapons will let you hit over the 9,999 barrier (It increases the damage limit to 99,999), and come with some nice bonuses on them. You'll also want to customise some armour to add Break HP Limit, that way you can have more than 9,999 max HP which is always nice, especially if you love numbers, and will give you the edge while fighting bosses etc.
If you'd like to try your hand at getting the celestial weapons, you can look here:
It should give you all the information you need to getting them, some are harder than others to get, but they're definitely worth the trouble in my opinion.