I'm confused on why you see this as more of a speed issue than an endurance issue.

If I use your numbers from above, it seems the baseline is an average of 100km by ~16km/h = ~6 hours
- Starting with that assumption approaching as a speed issue, imagine perhap 20km/h so now one might travel ~120km in the same time allowing for more margin overall on a 3100km trip to average longer days.
- Approaching instead as an endurance issue, if one extended cycling time to ~7.5 hours then one also gets to a similar ~120km in the same time.

I assume your 150km/day is more of an far end point (at least as far as averages) but approaching it *only* in one dimension would be:
- speed needs 24km/h to keep a similar time
- endurance needs ~9.5 hours to keep a similar speed
I suspect where you are pushing longer distances you'll likely push some of both but I also guess at least as much endurance comes into play since you want to do this in a repetitive fashion mostly day after day. Unless you have a much stronger constraint such as daylight hours or limited time windows [e.g. to catch ferries or with limited time windows like Logan Pass] I expect the longer hours in the saddle part will be at least as important.

As I've gotten older, my favored average distance per day has decreased e.g. first trip across US was 95 miles/day average including rest days, more recent trips closer to ~45-50 miles/day average including rest days. That is mostly because of taking shorter days than going faster. Hence for me at least, increasing my average distances/day would be more about increasing time in the saddle.