If DNS search engines are showing that your NS records are not fully propagating even after several days, there might be an easy solution. Here's my experience with SiteGround.
I recently built a website on SiteGround for a friend of mine. They already had a domain, registered through GoDaddy, so I used a temporary domain in SiteGround while I was working on the site (something along the lines of abc123.sg-host.com). Then, when the site was ready, I pointed their domain to SiteGround's servers by changing the nameserver (NS) records on GoDaddy.
SiteGround says "It takes roughly 72 hours until the changes in your domain’s records propagate". But after six days, DNS search engines (such as What's My DNS) were showing that the change had only partly propagated:

I contacted SiteGround who said "the propagation period should have definitely finished by now". They also told me to go ahead and change the primary domain in SiteGround from the temporary domain to the GoDaddy domain. "Once you make the primary domain change, an IP will be assigned to the domain and will also show up in DNS search engines."
I was a bit sceptical based on what I was seeing in What's My DNS and elsewhere, but I followed SiteGround's advice and updated the primary domain in SiteGround. This created an A record connecting my friend's domain to a SiteGround IP address, which I could see in SiteGround's DNS Zone Editor. Within five minutes of doing this, What's My DNS was showing that the nameserver change had almost fully propagated around the world:

I'm no DNS expert, but I wanted to document this for anyone else who finds themselves in a similar position. If DNS search engines are showing that your NS change has only partly propagated, this doesn't necessarily mean you aren't ready to go live. Try updating the domain name associated with your website (or, I suppose, adding the correct A record in another way), then checking again.
