My best advice is really a bit more general the kingmaker specific and I assume you probably know most already, from what I understand you have the following:
a 5 man group
fewer random encounters statically then indicated
a group of good roleplayers.
Your five man group is a bit more than the four average, so you could start by beefing up encounters by 20%.
Does the character in your group fit into the 15 point-buy stat range or are they higher? if they are increase the encounters even further.
Analyse your group to see what are their strengths, go to strategies, weaknesses and what do they avoid. Exploit their weaknesses to make the encounters harder, create unfavourable conditions to water out their strength a bit.
- Example: for my kingmaker group one of thir key strengths were an abundance of magic, one thing I found that put a bit more thought into how it was used and made it harder for them was an outbreak of cold weather (their exploring went well into winter) that forced them to spend quite a few spell slots of endure element (for themselves and their mounts).
Analyse your own strength, weaknesses and patterns for encounters and every now and then do something you wouldn't normally even consider, something off the bat.
If you are not rolling enough random encounters simply don't roll for them every time to catch up, if you don't want to do that toughen them up instead and create unfavourable conditions for the players, where they are forced to make less then optimal choices.
Remember the 20% resources spend per encounter by equal CR rule, and up the encounters to force them to use more resources.
Increase the number of times they can have a random encounter to say 5% every time the enter a hex, 5% per day and another 5% per night and finally a 5% chance of a natural hazard occurring per day (heatwave, cold snap etc).
the first book of the Kingmaker AP is to be a bit static, so look it through and make the opponents dynamic, think of it as a game of chess or Go, the staglord should react (badly) to their moves.
Example: After the river camp was taken out the players spend a bit too much time on other things then going straight for the staglord which resulted in that he had a party of bandits take over Oleg's trade station which resulted the players having to liberate it in a situation where they were actually heading back to drop off stuff and resupply making it a very difficult situation (which they solved by allying with the kobolds and have them dig a tunnel into the compound to allow for a diversionary attack from the outside with an infiltration through the tunnel).
Have some of the random encounters be something the players can't "escape" that is, rather than being able to run away before the encounter stats have them be the prey that walked into the clever hunter's trap. One thing is retreating from a pair of trolls you see, another is retreating when you are in their ambush, that is is someone down first round? it raises questions like how are we going to get that person out of here with us or do we leave that person behind to be eaten?
Change the fact of an encounter on them, when they think they have a encounter well in hand, throw in a monkey wrench, they are taking down some bandits with no problem? have a Owlbear or a pack of Thylacine attack or even just have the bandits receive serious reinforcements or maybe an old mite pit trap is triggered by a random player at some point in the fight.
Obviously they are doing more than well so you don't really need to be too cautious of them since they can handle it.
Hope it gave you a few ideas.