There will always be the argument between the endurance based runner and the speed based runner and which is the best way to reach a certain goal.
I would agree that all aspiring 10k runners need to have sufficient stamina to tackle the distance easily. This requires the ability to complete a 10 mile training run comfortably. I would encourage runners looking to break 35 mins to have a long run of up to 16 miles in the build up to a 10k race.
I would disagree though with the premise that you must work to build up the volume of miles and only then start carrying out any speed work.
Probably the most difficult skill for most runners is accurate pace judgement. To run a sub 40 min 10k, you need to average just outside 6.20 per mile. I would work with runners to practice this pace regularly so that , come race day, it is easy for them to set off at the correct pace.
I would also include some runs at faster than race pace so that race pace then appears easier. (I have a post on my blog about a training session that Russian runner Bondarenko used to use that outlines this principle)
The final thing that I would suggest that most runners are poor at is goal-setting and mental preparation. Most runners attached to clubs will complete races as part of a club championship and perform as best they can on a given day. Through better goal-setting and mental preparation, a stand out performance can be achieved.
40 mins for 10k is an excellent target to aim for and many runners, with the right preparation, will achieve it!
I would totally agree with Zanzinger over easy and steady state running - most runners run their recovery runs too quickly and hence do not achieve the recovery they were designed to elicit.
However, faster paced running where you are preparing for a race, I would wear a monitor and use it to record levels. This would be to see improvements in fitness or head off impending overtraining or illness. I would set the session though based upon race pace - you will have to race whatever the terrain or weather so you might as well get used to it in training.
I've got books supporting both training through pace and training through heart rate by some very well known coaches and scientists. My preference is for pace but find what works best for you!!
There are different schools of thought over the use of heart rate monitors and how best they can assist a runner. It appears you are experiencing two recognised factors that come into play with heart rate based training.
Heart rate drift - even when runners are very fit, towards the end of a long run, the heart rate will tend to drift upwards even though the runner is maintaining the same pace and level of effort. Hence, your rate rising at the 19 mile point.
The second thing is that a lot of external factors other than your exercise can influence your heart rate. Things about the run eg terrain, weather, time of day etc but also things unconnected like what sort of day you had at work, the domestic with your partner and even what you have had to eat can effect it.
My coaching preference is to set times/paces for runners and use a heart rate monitor to do just that - monitor and then use the information to determine training stress. However, I accept that other coaches use a heart rate as the most apporpriate measure of training intensity. If I understand your original post, you are running Helsinki in 20 days time and then Dublin 10 weeks later. I would follow through your plan of running 10 minute miles at Helsinki and then use the results from that race to determine pacing and training in the intervening weeks.