Question Upgrading 1.7.14 to current..

Did you read the last message of Greg? I'm missing the handling of PHP versions in your plan.
Your plan is to setup a new webtrees and export/import GEDCOM. That is ok, but then all information that is not stored in GEDCOM will be lost (users, news, tagged faces in images, ...). 
The other way would be a stepwise upgrade from 1.7 to 2.6.
In any case you have to install all the custom modules again.

As to PHP versions, yes, I can assign different versions to each site. And what I want is my existing site to stay on line until I am ready to launch the new site. So I was hoping to just skip all the intermediate upgrading by going straight to the latest version. But if I hear you correctly, none of the users, etc. would carry over, and this is why you are saying incremental. Is that correct? If so, then would this be the plan:
1. Duplicate both the current site and the current database, but just give them new names and adjust the duplicates config file to reflect them.
2. Begin a stepwise upgrade on the duplicate site until I arrive at the current version.
3. If there are any new entries I could just export/import the GEDCOM from the old to new site.
4. Any new photos added, I could just copy the old media file to the new install and that should solve that.
5. What happens if any new users register on the old site before the new site is done?

you want to move your data by export of a GEDCOM - file:
I simply would do no update at all.
Make a 2.2.6 version (and the used extensions) run,
and import
and copy images (may be need to adjust the linking to the images).
Let the users create themselves a new.

So your database has the recent structure (there is no need to step by step changing its structure to the current one, even if the change is done without user interaction).
You can test the result at any time and do not need to use a backup of your old data.
You will not need the software parts of 2.2.6 that are created only for compatibilty with some 1.x features. 

tthdoc wrote:

3. If there are any new entries I could just export/import the GEDCOM from the old to new site.
4. Any new photos added, I could just copy the old media file to the new install and that should solve that.
5. What happens if any new users register on the old site before the new site is done?

These are all imho actually arguments for not duplicating the site, but perform the upgrade on the live site.

You can see, there are several opinions about the best migration path. I tried both in the past and would prefer the way Bert suggested: no copy (you should have always a backup), go forward stepwise with your live system. If you like to read more:  wiki.genealogy.net/Webtrees_Handbuch/Anl..._der_Ausgangsversion
Especially wiki.genealogy.net/Webtrees_Handbuch/Anl...Anleitung_Upgrade_20 describes the advantages and disadvantages of both ways. 

Following the stepwise approach, you can check after each step if everything is still working as expected.
There are some steps where you have to check and modify your GEDCOM data, too.

for me the most relevant thing is the creation of the new database with UTF8-MB4 (utf8mb4_unicode_ci).

(afaik not mentioned in the german webtrees manual)

The issue is that I have done a lot of customization on the current site, and upgrading it would destroy most of it. So I would rather leave it live (as I said, not a lot of changes are made to it on a regular basis) and then upgrade a duplicate "live" site until it is the way I like it. Then when I make the switch, all the users are maintained (I don't want or expect all the users to have to re-register), and the "look and feel" that I created in the original site can be duplicated for the most part with customizations. The issue is it may take me time to do that, and I don't want to make these changes on the live site and if i make a mistake, the site is down. Given that, for me the way to accomplish it is to create a second "live" site, and then just go through the upgrade process. As long as no changes are made on the 1.7 original live site (in other words users are just "looking") I should be fine. Or am I still missing something?

I would not do so, but it is your site.

If you want to keep your users, keep in mind that there may be "no shows" and "not wanted" ones.
As we do not know your site and its traffic, we only can guess.

If they only want to see your data, they can do that for sure with the unmodified version 2.2.6 .

The change of the "look and feel" does not destroy data, so you can do it (and revert) at any time.

Why do you want to go live with a second site? I would never do, a chaotic mix is ​​to be expected. Create your modifications to 2.2.6, test them and when you are ready with that, take your data from the current site.
You can do that as often as you like, prior to a final release.

I would not actually have a "live" second site, meaning only I would know the url as a addon domain to my main site. So currently webtrees resides in a folder familytree in my main site, so xyz.com/familytree (but I have xyz.com redirect to xyz.com/familytree. So I would just have the duplicate site in familytreeupgrade, do all my incremental upgrading, make any mods and changes, and when satisfied, rename familytree to familytreeold and familytreeupgrade to familytree, and it should be a seamless transition.

That sounds ok to me. Go on!