I think your assessment is accurate. The text in the chapter all implies that the characters (possibly with the assistance of the NPC who arrives at the start of chapter 4) should be able to return quickly to Ten-Towns and potentially get ahead of the schedule, but this is not borne out by comparing the location of Sunblight on the map with the possible travel paces specified by the module, especially since much of the journey would be through mountainous terrain, which is even slower to cross! (By my estimation, the straight-line distance between Sunblight and Dougan's Hole is more like 12-13 miles than 16, but it doesn't make a huge difference to your math).
The timetable that the module gives, combined with the travel times given between towns, just about make this scenario make sense if one instead assumes that on sled, the party can make it back to Dougan's Hole in only a few hours (say 4h) - perhaps on the assumption that the friendly NPC who arrives to assist them happens to know a remarkably direct and easy path back through the mountains. Sticking to the roads thereafter, in that case they could conceivably catch up with the schedule at Easthaven, or get ahead of it by going directly to Caer-Dineval. (Remember that travelling by sled should reduce the listed times between towns by "up to 50%", and one assumes that has factored in any need for the dogs to rest.)
If we don't make this allowance, we must instead turn to the spells and abilities available to characters at this level (at best, 6th, according to the module) to see if they can get the party back any faster. Some options, such as fly and phantom steed, do enable individual characters to travel somewhat faster over some of the distance, but none of them really enable the party as a whole to move significantly quicker, with one significant exception:
The Ranger's Natural Explorer class feature
The Ranger's Natural Explorer class feature allows them to select a specific kind of terrain from a list and then enjoy many benefits while in that terrain, the two we're specifically interested in here being:
- Difficult terrain doesn’t slow your group’s travel.
- Your group can’t become lost except by magical means.
So when travelling in their favoured terrain, such a ranger's party will be able to move at their normal full speed and will never become lost. If the ranger chooses mountains as their favoured terrain, that obviates the biggest issue the party will have with getting back from Sunblight to Ten-Towns: navigating their way back across the Spine of the World. As they're unaffected by difficult terrain during this travel, they should be able to travel at a fast pace of 4 miles per hour; and as they're unable to get lost, they shouldn't have any issues with encountering impasses and needing to backtrack (though even if you were to rule they must still make those Survival checks, the Ranger will essentially have expertise on them due to another Natural Explorer benefit).
Now, even if we were to assume that the actual travel distance through the mountains is more like twenty miles, accounting for not being to go in a straight line, the party would be able to do that in 5 hours on foot. Having made their way down from the Spine of the World they're now only a few miles from Dougan's Hole and can make it there within a few hours by sled or on foot.
Things get even easier if your party has reached 6th level (which is appropriate for this part of the adventure), since at 6th the ranger gets to select a second favoured terrain, and this time they can choose arctic; this obviously applies all the same benefits as above to their travel in the tundra around Ten-Towns, so now they can go at 4mph in that terrain, too. Combining these benefits, I figure the Ranger's party can make it from Sunblight to any town in Ten-Towns in much less than a day, even if they stick studiously to the roads and don't take shortcuts (albeit requiring a forced march). According to the timetable of destruction specified by the module, they should easily be able to make it to Easthaven while it's still under attack or get to Caer-Dineval with a few hours to rest and prepare some defences.
If I were running this module, and the party didn't already have a ranger with these specialisations, I would strongly consider making available an equivalent NPC as a hireable guide or ally to provide this benefit to the party and enable them to travel the distance in reasonable time. Probably the least intrusive way to do this would be to have such a ranger turn up alongside the other NPC who already shows up with the sleds, ostensibly hired by them as a tracker to help them find the party in the first place. Even if the NPC ranger doesn't stick around after getting them back to Dougan's Hole, that at least gets them close enough that the travel times between towns become surmountable.