My initial thoughts on the system
I think they're a great first pass, though a little too complicated and a little sketchy in certain areas. I'm coming from the basis of familiarity with the rules in B/X D&D, though.
The "pace" thing seems overly complex and unnecessary, and yet also too abstract. It needs to be tied into movement speed in some way. In B/X, you basically moved at the rate of the slowest member of the party, and you had two 'paces'; regular exploration speed and running for your life.
Weather definitely needs to have an effect on getting lost. Even if it's just "harsh weather grants disadvantage to exploration actions." Possibly with a caveat about it aiding stealth checks.
There should probably be a foraging option, so desperate / ill equipped parties can find food and water.
I agree that the module would benefit from separation into "dungeon" and "wilderness" exploration sub-sections. I'm not convinced that this is a one-size-fits-all system.
Likewise, I also agree that a 6 mile hex is a better wilderness base, if nothing else so that it's more compatible with virtually every old hex map for D&D. Also 60 degree instead of 45 degree variations.
Exploration range on the 5 minute scale is way too fast. A party can traverse and "elf the room" with search checks up to 90 squares of distance at a moderate pace. 40 squares with cautious. That's ridiculous, IMO. Parties in Moldvay Basic D&D were lucky to get 18 squares on a given 10 minute turn, being assumed to move at the "cautious" pace, carefully checking for traps and whatnots as an entire party. And that's only if nobody was wearing heavy armor (realistically most parties would traverse 12 squares / 10 minute turn). That keeps the pacing to a more reasonable limit, IMO, as with 18 squares you're
much less likely to buzz through two or three average dungeon rooms in one turn of exploration.
I'd also love to see a sentence or two about discrete searches. Searching a cabinet that looks suspicious resulting in automatically finding the hidden door behind the false back rather than requiring a roll. That sort of thing.
The wandering monster table is... vague to the point of meaningless. The population density terms mean nothing, and are obviously meant to be universally applicable. I'd prefer to see something more concrete. I don't need actual demographics numbers but something better than what we have here. I also think the distribution on a d20 roll is somewhat unintuitive.
Even though I don't really want more complexity, I do think it's important to at least explain in the rules how a DM could modify the travel pace in the wilderness by the difficulty of various terrain types. One should probably not always assume that moving over volcanic mountains is going to be exactly as time consuming as moving through midland plains or cultivated farmland.
I'd also like to see monster reaction and morale rules. A simple d6 table for the former and a simple score and table for the latter would be fine, ala Moldvay.
Also I'd like to see more parts of the game have notational tie-ins to the new system. Everything from feat/class feature support to equipment. Bedrolls should note whether they provide an advantage or are required to avoid a penalty, for example. And it'd be nice to refresh the DM in this Exploration section on the duration of the standard light sources just to remind her that they now have concrete effects; torches last 1 hour (twelve 5 minute turns), lanterns last 6 (72).
All-in-all, though this is a very nice first stab and probably quite playable with a little jiggery pokery.
P.S. two more thoughts after posting:
I'd also like to see escape, evasion, and pursuit rules. Keep them simple, but I miss having the option to drop treasure or food to distract pursuing humanoids or animals/monsters.
Mandatory rest breaks. In Moldvay, the party had to stop and rest every hour for a turn or they'd start accruing penalties from fatigue. This nicely dovetailed with the need to light new torches. It puts pressure on the party to occasionally stop and reassess. Not super important, but something to consider.
BTW, the wilderness exploration rules in the Cook/Marsh Expert pamphlet took up slightly less than two pages, even including rules for air and water travel as well as variant terrain types (X19-X20).
P.P.S. Another small note that would be worth having in the rules is the intersection between "encounter speed" and the exploration system. In Moldvay, it was quite simple: a fight was assumed to take up a full 10 minute turn, regardless of its actual length. This was for neatness sake, handwaving the extra time as taken up resting from battle, dressing wounds, looting bodies, etc. The time taken on the wilderness scale was negligible. An similarly elegant interface between the sub-systems in Next would be appreciated.