I have recently downloaded NRaas Tempest and Longer Seasons. I altered the Seasons file to allow a season to be 92 days long. I also used Tempest to change weather and temperatures.

--Description Of My Setup--
I am playing on Alpine County, a coastal Texan city (if I understand correctly). Using my own modification to the Seasons, I made Winter 90 days long, Spring and Summer are 92 days, and Fall is 91 days long. Using Tempest, I made a weather "profile" for each month with that month's weather according to Houston. The year is now 365 Sim Days, but the "Epic" lifespan is 1,830 Sim Days (5 years). Is there a way I can make this lifespan longer? I found this mod Sims Life Age Mod (aka SLAM) V2 but it only allows 1,680 days, which is shorter than normal!

Does anyone have any advice for how to increase the maximum life-span?

I have sims on epic lifespan where 1 year is 24 days (so 1 season = 6 days), so the adult lifestage limit wasn't enough for me, what I did is manually change the amount of simdays for the lifestage in the Options.ini file to be longer than the epic limit. I guess you can do the same. You can find it where you keep your Electronic Arts/Sims 3 folder (where the mods folder also goes). Just change the number for each line that says "agingstagelength" +the stage like agingstagelengthyoungadult and add the total amount of sims days you want the stage to have, same for the pets. it should help you go beyond the limits without any mods.

It's not going to be practical for widespread use across a neighborhood of sims whom you never play, but I generally use Master Controller with the Cheats module to periodically reset the time in current life stage back to 0 for either my current sim or for a sim whom my current sim is allowed to restore youth to. (Or for a sim I want to keep around until my sim can meet them... It doesn't actually require my sim to have anything to do with it; that's just restrictions I place on the current sim so I'm not limited to just the occult types EA gave me.)

Although on Epic lifespan with the sliders adjusted as far as they can go, you've got a decent chance to catch and fix most of the sims in the neighborhood before they age up too quickly.

ETA
So you really can set the duration of an age category to be as long as you want it!? COOL!

Thanks! I will definitely try this the next time I load my game up!

It may seem like an absolutely INSANE idea; setting the lifespans for full 365 day years!
I will likely keep the younger life stages such as baby and toddler at lower levels (maybe a few months each, at most) as I don't really find them that enjoyable. It takes at most a couple weeks for me to have the parrent (s) do the teaching/training the kid's initial skills, and that's the end of the fun for me. However, the other life stages I want to set into the years for a couple reasons, actually...
One is simply to see how it works. I like to experiment. I also tend to just pick the game up every other month or so and play it practically non-stop for a month or more. I would like to see just how close to reality I can get the scale while still being enjoyable!

[Update]: Here we go!
I had closed my game to add in a couple mods I found that will help me with my current house in Alpine County (I keep wanting to just call the area Houston, even though the city isn't even close to Houston ).
Anyway, before relaunching, I found, and edited the Options.ini.
I went a bit off from the actual year, but I think it will work.
I made "baby" and "toddler" very short (7 days and 14 days, respectively). Child is 3,629 days (they turn into Teen at 10 years old, so I did 10x365, then took away the three weeks of baby and toddler).
Teen is until 18 years old, being 2,920 days. At 18, they become Young Adult until 32 (I wanted to give it a good amount of time, but leaving some room for Adult), making it 5,110 days. Adulthood lasts until age 64 (...and now, you can retire!) after 11,680 days! I think I set Elders to live into the 90s, but I can't remember the exact number now... TOO MANY NUMBERS!

Now, just waiting for my game to start up and see just how this "Epic (est)" lifespan goes!

"Epicest". I now declare that a word. Just for this occasion!

[EDIT]
Well, it crashed my game. I think I made the lifespans a bit too long...
It crashed before even showing the logo!

You can easily control the life span, in the resource Gameplay/AgingManager.

"resource Gameplay/AgingManager"?

I take it that you mean Game/Bin/Gameplay/GameplayData.package, then after opening it, AgingManager.XML?

If so, I found it rather quickly after reading you reply, and was quick to edit! Don't worry, I only ever started messing with it after copying it to another location, leaving the one in the game's files alone, so as not to break it.

Now, how does this actually work? I opened the .package with s3pe, and extracted the AgingManager.XML to open with Notepad++. Once I finish editing, do I import it back in to the package, and replace the default package with my edited one, or do I need to put the new one into my mods folder?

Also, I noticed that the life stages are actually based on year: "Description: number of aging years that a Sim is a young adult.". Under "kMaximumSimDaysPerAgingYear", I put "365". I assume this means a year is 365 days, and therefore if I set "kAgingStageLengthTeen" to "10", then Teen will last for 3,650 days? What will happen if I decide to try to edit these in-game? Will the sliders still be limited to default limits, or will they be longer now?

Well, I got it set up!
Turn out that if you do try to go changing the in-game sliders for lifespans, the sliders are limited to a set max, and because my changes go WAY over that on some of the stages, it is not possible to set them back after changing them in-game. Not an issue for me, though, as I don't ever mess with that anyway except to set them to max (with the exception of baby of toddler).

Also, something odd:
In the in-game options, some of the sliders do show inaccurate counts. For example, "child" shows 1,825 days, while it is actually set to 3,629...

Either way, it works. Thank you whiteman-Dara for pointing out the AgingManager file!

Someone at NRaas, I think, did that before (1 Simday equals one real day) and as far as I remember they used the options.ini approach. The reason why you crashed is probably because you did it in an ongoing game.
The game doesn't like it very much if you change the lifespans in between sessions. Some Sims might have been due to for an age-up and now they aren't anymore all of a sudden.
I also play with an edited options.ini where young adult/adult is 255 days but baby and toddler are shorter than the usual epic span (I set it to 15 and 50 respectively) and I often end up with toddlers with a negative age when I start a new game in a pre-populated world.