I had my party roll WIS (Survival) ✔️ for each hour of their travel

Set the DCs according to terrain they were traveling

Gave the proper modifiers to whichever Travel Pace they’ve chosen

Had the head of the Marching Order make the checks

Took nighttime & precipitation (being able to see stars) into consideration

Every 4 hours I rolled my d20 to see if I’d hit an 18 or up for a Random Encounter

Did my best to track everyone’s Food & Water intake

Eventually they tried Foraging but all decided to do it @ the same time

So ran it as a Group Check (which they all failed… several times)

Did I run this correctly?

I think I forgot to add Adv. to their Group Check for Foraging

Also, is there a specific time set for Foraging?

I added 15 minutes to the clock every time they Foraged

There's no set procedure for this in 5e. Tomb of Annihilation introduced wilderness survival rules, but they're not core to fifth edition. The Wilderness Survival Kit also has some good stuff but again, nothing as detailed as you'll find in the TSR-era.

I think what matters is you came up with a system and you followed it. And for what it's worth, I think you came up with a very good procedure.

Maybe you shouldn't run travel this way. Doing it this way tends to result in a boring playstyle where repetitive random encounters and survival checks turn the game into a drag. When I run travel (and I DM a lot of travel-based adventures), I usually follow this setup:

• Each character can engage in an activity. This activity might be navigating (from a map, using the stars, from a set of directions, etc), drawing a map, looking out for danger (+5 to passive perception to represent active efforts) or some other improvised activity. This does not include foraging, for a reason described in a bit.
• As long as someone proficient in Survival is in the group, I usually don't call for a foraging check unless food is scarce in the terrain.
• If prey is scarce, I include foraging as part of the travel. Foraging takes place with a "hunting party" being sent out. If finding food is high stakes, I might turn a simple foraging check into a "skill challenge" with several different skills being used narratively in order to determine success or failure. Usually, though, I ask for the leader of the hunting party to roll for it and for each member's WIS (survival) modifier to be added. If I skim over foraging, a hunting party is still assumed to be sent out, which splits the party.
• Navigating might call for a check with INT or WIS (survival) or with navigator's tools if it is difficult. For example, a navigation check might be necessary on a cloudy day if the party is using the stars to find their path. Usually, this activity can be resolved without a check.
• Drawing a map can usually be resolved without a check unless the area is unusually difficult to map, within reason. A particularly stupid party member can't draw a map, but most characters can do it easily if they concentrate.
• I generally do not use random encounters. The entire concept of "random encounters" as we know it is stupid and doesn't do its job. There is, however, a time and place for wilderness encounters. First, there are planned encounters, which might be stand-along, related to the story, or part of a travel side quest, but should be prepared to some degree in advance to be more unique and make more sense than "you see *rolls dice* eight goblins. Roll initiative."
• The second type of good encounter is an encounter that seems random. If you notice that the players are getting bored and want to fight something, or are feeling like there's no real danger in the travel, or you want to set the tone for a more dangerous area, throw a few monsters their way. These monsters shouldn't be any serious threat, just a little something to keep them on their toes and remind them that even during travel, the woods are full of monsters.

what matters is if your friends had fun and not what some randos on the internet think.

Obviously, I don't know your party, or your setting at the time so no answer is going to be perfect here. 

The one rule I set myself as a DM is to ensure there's always a good reason for a check. If there's a solid reason then I know the game isn't going to degenerate down to constant and potentially pointless rolling.

Being 100% honest though I hate travel. It always feels like one of the biggest challenges for me personally. I can quite easily manage camping/pausing/resting during a journey as I break it down into watches rather than by hour. I have the group assemble as a group with one person always taking a watch. That way, I'm making one roll for random stuff during each watch, and the players get to tell me what they'll be doing during each watch. I never feel like this is a great way to do this though. I guess what I'm saying here is that I can understand if there's something you're doing that's not terribly well defined in DMG or other sourcebooks I understand how easy it is to be self critical of the solution you came up with. 

The one question I would ask from your answer is what detail about the surroundings did you give your players? Did the players find somewhere they could climb high to survey the area? Did you give them a small running stream, or water source they could track along to find a village or other settlement? When dealing survival I'm thinking in terms of geography rather than mechanics. The old standbys then are what is high or low in this terrain. If it's a large empty expanse (like much of the US plains and deserts) getting either high into the rock formations to survey the terrain, or low into a canyon where a river might flow is a priority to track toward civilisation. If it's a dense forest like you might find in Scandinavia or Canada, it'll be about tracking medium to large animals to find their water supply. Once you locate a river, you're following that along to get to some form of inhabited area.

So mechanically, I don't see an issue. The question I would focus on is what did you give the players geographically to work with?