I am just spitballing obviously, but the way i envision the system is something like this:
The PCs are setting out on a journey. The journey will have a number of "legs" -- a "leg" is defined by a discrete environment. For example, the part needs to go from town to the dungeon in the mountains and this journey has three legs: a couple days on the road, a day through a haunted forest, and then three days in the mountains.
Each leg has a Difficulty rating and a Threat rating based on how dangerous the environment is, which is a combination of both the probability of random encounters and terrain effects. Difficulties range from 10 to 25. This is the skill check target number. threats range from 1 to 4. This is the potential travel damage for the leg. For the above example, assume the following: Leg 1 10/1, Leg 2 15/4 and leg 3 20/2.
Every day of travel, the party must make a check against the difficulty of that leg. Here you might use the environments random encounter chart for inspiration as to what kind of check to make based on what kind of obstacle is present. Every PC makes a check for the day. Success reduces the Threat by 1. Once the Threat is at 0 no more checks need be made. It gets a little metagamey here, but since we are trying to dispense with time consuming encounters we are already deeply in metagame territory: a PC can't make another check, even on the next day or next leg, until all the other PCs have made one (this is to keep the ranger from jumping in every time).
So, the example journey includes two DC 10 checks, a DC 15 check and 3 DC 20 checks. Each time, the party works together to reduce the Threat to 0.
At the end of the journey, all remaining Threat is added up to determine the Travel Damage taken, which must be "bought off" by each PC with Exhaustion levels, spent Hit Dice, used up daily abilities and spell slots, and so on. One would have to work out a good conversion for each resource.
Again, that's all very bar napkin sketching but I think it is the seed of a good system.