There's a few problems which the approaches you describe:
Character Creation: Roll your stats as normal once. You may choose to use what you roll or build your characters stats using 32 point buy method described in pg. 169 of the Dungeon Masters Guide.
This is a common mistake in homebrewed rolling methods; but a rather serious one. Any rolling method of any kind becomes completely illegitimate if the player isn't forced to accept the results that he rolls, good or bad. If the player is allowed roll again whenever he rolls poorly, rolls below the average, rolls much worse than the other players, doesn't roll well enough to meet his character concept, or simply doesn't like what he gets, then the entire concept of rolling becomes a sham. In fact, groups who include such "safety nets" against anything but, perhaps, the most unworkable results are simply admitting, implicitly, that rolling ability scores is too random a method and that serious steps need to be taken to curtail randomness in something as fundamental as character creation. They are, essentially, admitting the great importance of the key virtue of point-buy.
In your case, you're using a variant of the "reroll if you roll below average" rule. You've said, in effect, "Every character should be at least as powerful as one built with a 32 point-buy and should give you at least as much ability to meet your character concept as you would have had with a 32 point-buy. Thus, if you happen to roll worse than that, just make a completly new set of ability scores using 32 point-buy and pretend your rolls never happened." So you're completely invalidating the whole idea of rolling by not requiring anyone to accept his rolls unless he likes them. If he doesn't, he can just go ahead and choose pretty much any ability scores he wants anyway.
Yet in this particular case it gets even worse. Some people use a method similar to yours; but they add the important requirement that the player must choose whether to roll or use point-buy
before rolling. That is, he must accept what he rolls whether it's good or bad. If he's not willing to take that risk, he can opt for a predictable point-buy instead. In your case, the player is allowed to roll, see what he gets, and
then decide whether to use point-buy instead. The result is that no one is worse than a 32 point-buy character; but anyone who rolls lucky will be significantly
better than that, thereby preserving (albeit to a somewhat lesser degree) the same old problem of unequal and imbalanced PCs.
That actually hints at another serious problem with the rolling methods most people use. Most such methods include some critical minimum above which a player must roll for his results to count. If he rolls below this minimum, he is officially entitled (or even required) to roll again. The 3rd Edition 4d6 method, for example, included such a critical minimum. The problem is that very few such methods have the necessary critical
maximum to go along with it. If you're going to permit someone who falls too far below the average to roll again, then you damn well better
require anyone who falls too far above the average to roll again. Having a character above the 90th percentile, for instance, is just as bad as having one below the 10th percentile. I was, on that note, very pleased to see that the 4th Edition version of the 4d6 method has added such a critical maximum, requiring those who roll
too well to start over. This was something 3rd Edition lacked.
Roll for your Hit Points as normal. If the total of the hit points that you have rolled is less than the total average of the hit die of your classes above 1st level (3.5 for d6 for example), use the average. Any half HP from the totaled average rounds up.
Here we have the same problems. You're basically letting people roll; but letting them ignore any bad results as if those rolls never happened, thereby making the entire rolling method a sham. Yet at the same time you're unbalancing things by allowing them to keep the good results whenever they get lucky. Getting to keep good results but ignore bad ones will only result in PCs having substantially more HP than they're supposed to have for their level.
Both of these rules protect the player from low dice rolls that would affect them for the entire campaign
Correct. (At least relative to the "standard baseline" of the game's mathematics; but not relative to the scores of other, luckier, players.)
while not granting those who roll well any more benefit.
Very incorrect.
On the contrary, granting those who roll well a large benefit is
exactly what you're doing. The only way to allow people to ignore low results without favouring those who get lucky is by also forcing the lucky ones to throw back their high results. But if you're going to ignore the low results and throw back the high results, everyone will just end up with average values. And if everyone is going to have average values, you might as well just use point-buy in the first place, since that's exactly what the point-buy system is designed to facilitate.
