I would go ahead and do this. You have nothing to lose. You do not live in Alaska.
The CLR Method works just fine. It is not the CLR that you are worried about making a hole in the heatercore, it is the pressure you use with a garden hose that may be too high. Always use a steady stream with no real pressure.
I cleared out my heatercore using the 2nd link you provided. It is by far the most effective method. I stupidly bought my car with no heat. Forgot to check as this is Miami,FL. Never dips below 65f.
On Top of that, Previous owner mixed Green Coolant with VW Pink Coolant. These two together creates a brown sludge that can destroy radiators. Never Mix these two. I ended up buying a new $25 coolant tank as mine was extremely gross. I could only imagined what it looked like further down the system.
You may also want to complete a full Coolant Drain and Flush before this. I used Prestone's Flush/Cleaner product. This was really good as it took 1 Treatment and 2 additional water flushes to get rid of all of my radiator's iced tea colored muck. It eventually drained to a nice clear color. (make sure you use the 5mm engine block drain plug, and not the plastic radiator plug.) This is where all your dirt lies, poke it with an allen and watch crud fly.
This is what gets trapped in your radiator and heatercore. A proper flush will make your later heatercore flush safer as you have reduced pressure and particle size. Plus, clean coolant is a nice bright pink color!
Attempt the heatercore flush while everything is drained before your final coolant fill. Just so you dont spill shit everywhere.
Caution, Inlet and Outlet pipes on the heatercore ARE PLASTIC. You know what happens to 15year old plastic. Go buy a $1 hose pick and gently work the hoses off.
Then, do what ChrisFix mentioned. The Garden Hose backflush method. This is always a temporary week long fix that needs to be followed with CLR. This is only to prep for CLR.
Second, do the CLR drill pump method. I even used a 60clr/40wtr dilution as no fucks were given.
You will want to send water in the outlet and out the inlet (backflushing dislodges crap as opposed to pressing them in further. Make sure you use $1 Teflon pipe tape to make sure all your fittings on your pump are snug and you are not pumping in air.
Loosely tie a Cloth or a bandana with a rubber band or zip tie around your inlet tube in the bucket to act as a filter.
Pump for a mere 5-10 minutes, and go sit for 30. CLR needs to soak into the calcium deposits. The pumping is mainly to get the CLR to the sweetspot+some back flush pressure.
Repeat the pump and sit about 4-5 times.
Get clear hoses so you can watch in disgust as brown stuff swims down your lime green CLR.
Purge out all CLR with garden hose until it runs clear.
Now, Connect your hoses and refill your coolant. You are using Distilled Gallons of Water with G12/G13 Coolant Right??
(Keep cap open). Get ready to open a bleeder screw or two until air bubbles disappear from the screw opening and a tiny stream flows. (This means theres no bubbles in your lines,[air insulates, not transfers heat])
Crank Your heat up to high and feel the goodness.
I typed this up real quick and may have left out stuff. Please reply if you have any questions. Ill be sure to answer.