Apply advantage/disadvantage to passive Perception.
There are rules for applying advantage and disadvantage to passive scores (page 175 in the PHB):
A passive check is a special kind of ability check that doesn't involve any die rolls.... Here's how to determine a character's total for a passive check: 10 + all modifiers that normally apply to the check. If the character has advantage on the check, add 5. For disadvantage, subtract 5. The game refers to a passive check total as a score.
For example, a character whose passive Perception score is normally 18 would have a score of 13 if they are currently suffering from disadvantage on Perception or a score of 23 if they currently benefit from advantage.
Applying advantage and disadvantage to Perception in different scenarios, especially when it applies differently among the characters, is an easy way to avoid the determinism of passive scores by ensuring that, on occasion, characters who are normally the best at Perception will be surpassed by those who are normally worse or the worst. You can apply advantage and disadvantage secretly to preserve some of the surprise or publicly so the players know what they are getting into.
Importantly, this does not require any extra rolls or homebrewing: it makes use of the existing rules for passive scores. All it requires is a quick judgment followed by some mental math.
As long as you are fair and reasonable in assessing the scenarios in which to apply advantage and disadvantage, you will not be nerfing characters who have good Perception. Rather, you will be offering variety and a chance for the other characters to shine. When possible, focus on giving advantage moreso than disadvantage (notwithstanding the Darkvision example below, which is the most common scenario). It is better to make a few players feel empowered than to make a few others feel disempowered.
Example applications of this technique.
If you have a party in which some characters have Darkvision and others don't, you can make use of dim lighting. Everybody can still see in dim lighting, but those without Darkvision have disadvantage on Perception involving sight. If the characters who usually have the best passive Perception scores don't have Darkvision, their scores will be reduced in dim lighting. Since many dungeons are dimly lit anyway, this allows those with Darkvision to pick up the slack.
Other reasons to confer disadvantage on a player's Perception might be that they are too far away from a trap to notice it, or they are too distracted at the moment by something else to notice it, or they are so unfamiliar with the nature of the trap that even though they notice it they don't actually perceive it as a threat worth paying attention to.
Some reasons to confer advantage on a player's Perception might be that they are especially close to the trap, or they are currently assigned to paying attention to traps while the others go about different business, or they have prior knowledge or experience that makes them more likely than the others to perceive the trap. You could also consider giving a character advantage if they decide to use class features or spells that should reasonably improve their chances of noticing a threat.
Note about other passive scores.
You can apply the same guidance in this answer to other passive scores, such as those for Insight, Investigation, and Stealth to prevent monotony there as well.
My experience using this technique.
I have applied this technique in most dungeons I have DM'd across several campaigns. I have found it much simpler than rolling active Perception checks on a regular basis. Generally the player with the highest passive Perception score will be somewhat surprised the first time they are not the first to notice something. Usually the only overt confusion is due to players being unaware of the rules for dim light, an unrelated issue. In either case, once players understand the rules, they tend to take the technique for granted and respect the results, so things go smoothly.
I also use this technique regularly for passive Insight scores. The results at the table are similar, except that usually players do not notice it at all because they do not typically realize that passive scores other than Perception even exist. I occasionally use this technique to modify passive Arcana, History, Nature, and Religion checks, taking into account what I know of each character's background before declaring whether somebody is intelligent enough to have known a particular piece of information. However, I don't think determinism is quite as much a problem for Intelligence-based skills.