It really comes down to what your goals are. If it's to become a strong recreational rider, do centuries on the pointy end, and maybe a race or two. that's one kind of training. Doing lots of endurance, tempo, and hill repeat work is a fine place to start. But if you want to get your license and hit the racing circuit hard, then that's almost the opposite of what you'd want to be doing. It's easy to say that you (and I paraphrase) "just want to get stronger", but there's a right way and a wrong way to do that depending on what the end goal is.

The Cyclist's Training Bible - Joe Friel
The Time Crunched Cyclist - Doper Carmichael
Training and Racing with a Power Meter Second Edition - Allen and Coggan

Friel is very in-depth with page after page of geeky numbers and theorems. Tough to digest, but if you can understand at the 10K foot level you did well. TCC is a good overall mid-level view of training for recreational riding as well as racing. It has good information whether you are time crunched or not. A&C is my favorite reference. It is useful with or without a power meter. Before I employed a coach I used their plan as my pre-season prep.

The 5 and 20 CP tests are for power. Friels' test is for LTHR. The protocols are different because you're measuring different things. When you start an interval at constant power your HR starts low and rises. Relatively quickly at first then after a few minutes the slope changes and it rises more slowly. There are two different things going on- first is that HR lags effort. Do a short sprint and see that your HR doesn't jump up to your max as you sprint, in fact it'll keep rising after you're done. The second is that once HR has caught up, there's "cardiac drift" which gradually drives the HR higher, even with the same power output.

I see this when I do an interval that's 45 minutes long at a constant power of 230 watts. My HR will be 120 or so at the start. It'll rise to 145 in a minute or so, then for the rest of the interval, gradually rise to 160.

The LTHR test is a 30 min effort to ensure that your HR has passed the lag period before the measured portion (and I think the test is taking cardiac drift into account as well). I think the first 10 minutes of effort also serve to burn off some anaerobic capacity so you're measuring less of that and more aerobic. Most power testing protocols for 20 min include a short interval before the test to do the same thing.

Now that's funny!:D

Heart Rate and Cadence
 

The other effect on heart rate is cadence. In general, a faster cadence will increase heart rate for the same power produced. Lower cadence requires more torque and thus more strength for the same power produced. Hence beginner and returning cyclists (I am not using the word weaker since we do not want people to visualize themselves as weak) rely on their strength since their cardiovascular system needs development. So they tend to spin slower.

However, relying on strength results in the legs loading up with fatigue. This effect will be more pronounced climbing.

So if I climb Old La Honda at higher cadence, my heart rate and breathing rate will be higher for the same climb time. If I climb it in the big ring, my heart rate is lower but the time will be about the same but my legs will be dead at the top. Of course they are always a little dead at the top of OLH.

So the other thing newer cyclists can do is keep the cadence up. So when you climb the easier NorCal hills such as climbing Alpine Road, keep the cadence up. I can climb Alpine at 95 to 100 cadence. When I started out, I thought it was tough to climb and generally did 75 to 80.

Spinning faster is another technique that takes time to master. However, the ability to spin fast is a competitive advantage.

Cadence is adaptive for some people too. If you train at 100 RPM often the body will respond after a few months of this by no longer producing a higher heart rate for a similar work load.

got it.

I'm actually not sure what my goals are, but given available time and such, 'strong recreational rider' is probably a more appropriate goal for me for now than 'rabid racer'. I was on the threshold of the racing plunge in high school, but never really got started, so I'm intrigued and want to check it out, but I think my fitness would be too big of an issue at this point.

Then my advice to you would be to take a look at the TCC plans for a recreational cyclist that best fits your mold. Train for three months using one of his plans, then try racing. You'll get a feel right away if it's for you. Racing is addictive behavior in most sane people.

Even bike riding appears to be highly addictive... thanks.