@Varun M., I am born and raised in the Sunset so I know quite well that you want to go somewhere more sunny! I thought it was interesting no one in the other thread liked the idea of moving to a duplex. I would say to take your wife to open houses and get a feel for what is out there. If your wife doesn't like anything, then staying put and pulling equity out to invest is an option, unless she wants to move and buy another SFH somewhere else to live in. Primary residences are so personal that they are sometimes tough to form an investment decision on.
If you are set on pulling money out, first thing is to look at your current primary loan terms. If the interest rate is low, thats great, if not, you could consider completing a refi or cash out refi on the primary loan. It will be easier to do so now than after getting a HELOC/HEL as your rate will be slightly higher trying to keep the HELOC/HEL while refi'ing the primary loan. I think you hit some of the main points on using HEL/cash out refi vs HELOC. I would add that usually HELOC's are interest only so your monthly payment will be lower than a principal and interest payment for HEL/cash out refi.
Getting one over another depends on your investing outlook, what you are investing in, how comfortable you are with variable rates, and tax considerations. Some like to use a HELOC for flipping as they pay back the money once the flip is complete. Some like HELOC's because they are interest only and also the interest is tax deductible if used for business purposes (ask your CPA). Some are comfortable with a variable interest rate as rates continue to trend downward. Bank, credit union, mortgage broker, it doesn't matter, just make sure you go with someone with favorable ratings.
In my case, I took a cash out refi of my primary due to the low interest rate and invested the money into a 14 unit building in the South Bay with some partners that we just closed on. We will be investing for the long term so I don't have any issue with getting the longer term debt. Yes, the money did sit for a bit as the timing wasn't perfect but neither is life!
Leveraging up your primary residence is a personal decision. Questions to ask yourself are if you are able to service the larger debt payments on your own if the investment goes south? Is your spouse comfortable with higher or a certain amount of additional debt on your primary? The lender on your investment property 1-4 units, will consider the additional debt payments but also the potential rent (i have heard anywhere from 50-100% of rent depending on the lender) on the property to calculate your DTI. Commercial lending would be a different story.
There is no one right answer for everyone's situation but it sounds like you are asking the right questions and you'll do well. Biggerpockets can offer a lot of opinions, its up to you to shift through and decide how you want to invest and how it will fit into your lifestyle. Investing is not all about the numbers either, there are lots of intangibles that don't make it onto a spreadsheet and yield calculation.