You're making characters (as opposed to the players) choose between two "indistinguishable" activities that have different outcomes. Yes, that's being inconsistant
Incorrect. I am acknowledging that the player's choice (a game play element, which type of rest to take, and for how long) and the character's choice (a narrative) do not have to be intimately linked.
The player is making a choice what kind of rest to take, and there are different rules implications for each. The character isn't making any choices because they are a fictional entity, but the narrative that the character rests is the same regardless of which type of rest the player chooses.
Ok, I'll change the hypothetical. There are three characters: a fighter, a wizard, and a warlock (with both spell slots remaining), all at 1 HP. They declare they're taking a long rest. After 8 hours, they get up. The fighter breaks camp, the wizard prepares a new spell list and casts a spell, and the warlock cooks a tasty breakfast and casts two spells. This takes 30 minutes. Afterwards, the two casters harrangue the fighter into resting so that they can be better prepared for any danger on the road. 30 minutes later, the party is ambushed. The wizard, by definition, is at full HP. How many HP do the fighter and warlock have? Was making breakfast and breaking camp for 30 minutes enough to finish their long rest to get their HP back? Or by resting again with only a 30 minute break (insufficient to interrupt a long rest) are they still not finished with their long rest? Do your answers change if there was only 5 minutes of non-rest activity instead of 30 minutes? How about a full hour?
This hypothetical is better constructed, and I can answer these questions.
Firstly; intending to end one rest, do very little of note, and then return to rest is an attempt to game the system and just plain doesn't work by my interpretation - even if the players is insistent that they have chosen to end a long rest, cast some spells, then start a short rest, it is resolved as casting some spells during a long rest.
That means that this scenario probably doesn't include anyone harranguing anyone into more rest than necessary because there is no benefit to be gained from it. Which means that the ambush happens after a long rest has ended and the party has started their adventuring day.
So specifics on the remaining questions: Making breakfast and breaking camp for 30 minutes is not ending your long rest if you intend to rest more afterwards. My answers do not change if they only took 5 minutes of non-rest activity, but do change if a full hour is taken - specifically, if the characters interrupt their own rest for longer than an hour while they intend to return to rest, they've spoiled the long rest and have to start again. So it is much more beneficial to the characters if the players actually stop intending to rest and do something else than it is to try and game the rest mechanics.
I will acknowledge that my interpretation does produce results which may be referred to as "weird." However, I find this to be a case of weird results no matter what you do, so the choice is really which weird results you would rather have; my weird results of the players being encouraged to have their characters rest the minimum amount of time and then go do stuff, or the weirdness of trying to rest and not succeeding if the player insists on doing that to them self - or the weird results of being able to do things like use second wind, short rest, use second, short rest, and repeat, or a warlock that has gained access to the cure wounds spell full healing an entire party with numerous repeated short rests. And I choose the "No, stop that, no cheesing, play the game" weirdness every time.