Handling witty jabs at the DM

Passive checks are your friend

First, you can probably replace nearly all of your checks with passive perception (PHB 175):

A passive check is a special kind of ability check that doesn’t involve any die rolls. Such a check can represent the average result for a task done repeatedly, such as searching for secret doors over and over again, or can be used when the DM wants to secretly determine whether the characters succeed at something without rolling dice, such as noticing a hidden monster.

This is usually done for perception, but you can also employ these for things like stealth as well. Passive checks let you automatically deal with all of those... passive rolls.

Only call for rolls when they matter

DMG 237 sums this up nicely:

Remember that dice don't run your game- you do. Dice are like rules. They're tools to help keep the action moving. At any time, you can decide that a player's action is automatically successful. You can also grant the player advantage on any ability check, reducing the chance of a bad die roll foiling the character's plans.

Parse your dungeon crawl into specific scenes

You can avoid repetitiveness by clearly delineating the dungeon crawl into individual scenes. You allude to this issue when you talk about a dungeon that's only rooms. Basically, instead of thinking of the dungeon in physical terms, you should think of it in game scenes, and gloss over the unimportant parts.

For example, in a dungeon crawl I've run in roll20, sometimes I will just reveal a hallway or an empty room and say "there's nothing in here". Likewise, I don't move avatars or reveal areas on the map until it's actually relevant--I only use the map when the map is necessary. Doing so saves a lot of time that would otherwise be wasted rolling dice for no good reason. You can still create a sense of tension by throwing in a handful of red herrings, too.

Once your dungeon is set into scenes, you can make scenarios that matter. Instead of having your players stumble through a dark cave, rolling along the way, you can say "You grope through the darkness for a time, making good progress. In the distance, you notice the glow of a campfire...". You might notice that movies do this a lot: a character might be navigating a cave or dungeon, but viewers don't see all of it--only the parts that are somehow significant.

By viewing your dungeon as a series of important scenes, you can make every die roll somehow significant, and therefore streamline your dungeon crawl.

This is exactly what the advantage/disadvantage mechanic was made for.

Let’s consider the Help action:

Alternatively, you can aid a friendly reature in attacking a creature within 5 feet of you. You feint, distract the target, or in some other way team up to make your ally's attack more effective. If your ally attacks the target before your next turn, the first attack roll is made with advantage.

In combat you can distract a creature to give your ally advantage on their first attack roll. It makes sense that a distracted creature could also have disadvantage on a skill check if they are distracted.

Or you could simply increase the DC of the checks. If a task is normally easy with a typical DC of 10 then maybe the distraction bumps it up to a medium DC of 15. If the DC for the task is normally 15 then the distraction might bump it up to 20.