the more you do trying to meet the bar the more things start pulling apart at the seams. I agree that there's lots of ways to "fix" the problem ranging from spree killer body counts to loldeadly monsters by tinkering around the margins like higher CR encounters & more monsters or playing with rest mechanics, but all of them create their own set of problems & some of those problems need their own tinkering to fix.
As to tiny hut, yes the GM can effectively troll the players with a weirdly high number of burrowing/incorporeal monsters that thwart tiny hut just as they can introduce an incredible gathered force waiting for it to end or continually somehow interrupt rests until they say fiiiiiine & give in. At the end of the day it's still a cascade of things that are the result of the badly set bar that initially started things & the risk of having a rest interrupted is basically "whatever lets take another rest".
You are going to extremes here. There are ways to link random encounters without resorting to extreme measures. The trap is not to roll each day separately but to roll the whole trek at once. Then you link them (more or less) together to make a short story. Most travel time should be easy trekking in the wilderness. Not every single day should have encounters. I usually either put encounter near the beginning or near the end.
For example, on a 20 day trek. If we assume 8 encounters; most of them in the middle of a forest toward a lost cavern, reputed to have a dragon in it. I rolled these. Total party average level 7th...
1) 15 goblins with 1 boss.
2) 7 Bugbears.
3) A young green dragon
4) 11 Hobgoblin
5) 2 displacer beasts
6) 22 hobgolins, 30 goblins and 1 hobgoblin captain
7) 6 Berserkers
8) 3 veterans.
I decide that the players will see our three veterans being under attack by the 7 bugbears. They can rescue these or not. I make the veterans a group of dwarves going toward the mountain to check if a mine could not be built. Since I rolled a lot of goblinoids, I decide that the hobgoblin captain encounter will be linked with all goblins in the vicinity. I make sure that the last bugbear will swear on his dying breath that Uktuk (or whatever name i would come with) will take revenge.
The fight will be witness by the two displacer beasts (a mated pair). These predators will wait and will start to follow the characters and the dwarves (if both sides joins) or the players only. Encounter 1 will occur a few hours after the first with the either the boss or one of the goblin attempting to flee toward the main camp. After 3 rounds of combat, Encounter 2 will come to the aid of the goblins. The displacer beasts still keep at bay.
Once all this is over and done, the party will surely take a short rest, this is when they will see the green dragon. The dragon will not attack. It will only pass by the party. The goal here is to have the party see the dragon in the distance. This decide me to make the dragon an offspring of the bigger one. After all, people can make mistakes about the color of an adult dragon or that supposedly blue was killed by a green one with a few of its offspring.
The character will probably track the goblinoid's traces to their camps. This is where they will get encounter 6. I decide to make it a base camp with 3 towers with a wooden palissade. No buildings but tents in the camp. When the players are about to win the fight, this is where the berserker from a nearby tribe will attack both the players and the hobgoblins (a party ready to use diplomacy will get away from this fight). If the players make peace with the berserkers, they will learn that these hobgoblins have been preying on their tribe for sometimes now. These hobgoblins used to fight for a blue dragon but that blue recently got killed by a big green dragon.
Once the players "win" both encounters, if they have exhausted their resources, and the berserkers are gone; this is when the displacer beasts will attack, just before the ritual for the Tiny Hut ends (if any). If not, in the morning, the young green might attack (or not) and at the end of that fight, the displacer beasts will.
This is quite easy to do, takes about 5 seconds of thinking (but a lot more to write for a forum) and the enoucnters are all goods, can be used to give hints to the players and opens Role playing opportunities if they want to.