I'm trying to transfer my public DNS provider but I have questions since my current setup seems odd.
First, my registrar (some small co.) provides my domain name registration but no DNS hosting. Only options to specify NS hostnames. My DNS hosting is my ISP, no web portal access to zone file for modification (thus the desire to move).
Second, I need to switch to another provider which will allow me to manage my zone file (i.e. dns.he.net, cloudfare, etc). I was told that once I created a zone file with the new provider, I need to make sure my NS records point to the new provider's NS. I believe this needs to be done at the registrar.
My question is do I need to change my NS ONLY with the registrar and wait for propagation or do I need to change NS on BOTH the registrar AND the ISP? Also, should I do anything about the SOA records?
Note that I could transfer the registrar as well (i.e. with GoDaddy transfer service) but the question remains if I need to change the NS in the ISP's zone file for my domain as well. Thanks!
You've stated your problem well. You also have all your facts right.
So, to answer your question, NO there is nothing you need to do with your ISP after you change the NS settings.
If you want a suggestion, I would follow the option you already suggested to transfer the domain to another registrar that also does DNS. I'm not going to recommend GoDaddy, but it is certainly a valid option. There are plenty of others.
If you want to avoid any downtime, make sure you have all the important DNS records replicated at the new host before you transfer or change the settings at the existing registrar to point to the new DNS host.