Strategy after Navigation

If you still care about your production of other resources, the optimal strategy is probably to sacrifice your faith immediately before resetting the game as a whole, and only then. Sacrificing your faith at any other time (especially if you've sacrificed it before) will give you a large hit to your general production in exchange for a small boost to your total faith generation, which probably isn't worth it.

If you really only care about sacrificing as much faith as possible in the end, then it gets murkier, and as you said, the math is complex. The only thing I'm sure of is that you shouldn't sacrifice your faith if the production bonus from your faith is lower than your faith bonus due to sacrificing, unless you're about to reset the game as a whole. I would probably sacrifice once my faith production bonus is double my faith sacrifice bonus (but again, only if I'm willing to cut most of my other production to speed up faith generation).

Edit: At some point after this answer was written, the faith bonus was nerfed: it now begins to suffer diminishing returns at 750%, and is hard capped at 1000%. If you're able to store enough faith to quickly get your faith bonus over 750% after sacrificing faith, then it makes sense to begin sacrificing faith often. (The Apocrypha bonus has no such diminishing returns.)

Okay, I did some of the math myself, based on the formulas from the Wiki and on the source code of the game.

The answer is: Yes, it is worthwhile to reset, even after getting near the 200% paragon productivity cap. Read on for more details.

Paragon

Productivity: The productivity boost is quite easy. It is capped, so you will never get more than 200% productivity out of it, unless you research tings that say "Improves paragon effect and scaling by x%". This will raise the cap to (200+2*x)%. These techs cost a large amount of paragon, stating at 500 and going up to 1750 at the time of writing.

Storage: Every 100 points of paragon provide a 10% storage bonus, which is not capped. So if you have 1000 points of paragon, your storage will have doubled. This is also increased by the upgrades mentioned above. So for this alone it is useful to have lots of paragon.

The relevant parts of the code are in prestige.js. Here's a bit of pseudocode which is a bit more readable than the original code. The getHyperbolicEffect function does the capping and is explained in another answer.

getParagonRatio: function(){   
    return 1.0 + paragonRatio;  // paragonRatio is from the mentioned upgrades: 5% = 0.05
},

// This value is multiplied to resource production
getParagonProductionRatio: function(){
    return getHyperbolicEffect(paragon * 0.01 * getParagonRatio(), 2 * getParagonRatio());
},

//every 1000 paragon will give a 100% bonus to the storage capacity
getParagonStorageRatio: function(){
    return (paragon / 1000) * getParagonRatio();
}

Karma and Happiness

This one is not so obvious, and the graph from the wiki is actually a bit misleading, because the x-axis is in KarmaKittens, not in actual kittens. So I've done a few graphs in LibreOffice, which show the relationship between population size and Karma.

Resetting once: This one shows how much Karma you get when you reset the first time at a specific population size (orange curve, top, left axis). For example, I reset at around 210 Kittens and got 23.x Karma. As you can see, this curve is roughly linear with a few bumps although the formula contains a square root. This is because the formula for KarmaKittens (blue curve, bottom, right axis) crudely approximates a quadratic curve.

Resetting multiple times: Here you can see how much karma you get when you reset multiple times at a specific population size between 50 and 500, from bottom to top. Okay, 500 Kittens is a bit utopian, but still.

You can see for example that if you reset at 150 Kittens (somewhere after Concrete Huts), you'll have 30 Karma after your 4th reset, 40 Karma after the 7th, 50 after the 11th, and so on. You can also see that resetting with more kittens is much more effective than resetting often with fewer kittens. However, for a meaningful comparison, you would have to factor in the time it takes you to get to such a large population size.

More resets: If you are really patient and reset the game lots and lots of times, here's the same graph up to 50 resets:

Update: Karma over Play Time

Nikana Reklawyks logged the kitten count during his "somewhat idle" game with 400 Paragon & 60 Karma. The following plot shows how much Karma he would have got from resetting at any point during that specific game, for different initial amounts of Karma.¹

^{1. Of course, this graph does not account for the fact that you would get kittens a lot faster or slower depending on the initial amount of Karma.}

For example if you had 50 Karma (the green curve, third from the bottom), you can see that at the end, after 216 Hours with 440 kittens, you would have 69 Karma after resetting. However, after the first 120 hours at 400 Kittens, you would already have got 66 Karma. So you spent the last 100 Hours for roughly 3 points of Karma and 40 Points of Paragon.