OpenWrt

OpenWrt's ddns-scripts package supports a custom update URL with HTTPS. Install the packages (OpenWrt 21.02 and later):

opkg update
opkg install ddns-scripts luci-app-ddns ca-bundle curl

Configure (UCI)

Add to /etc/config/ddns:

config service 'justasrv'
	option enabled '1'
	option service_name ''
	option lookup_host 'acme-main.ddns.justasrv.com'
	option domain 'acme-main.ddns.justasrv.com'
	option username 'acme-main.ddns.justasrv.com'
	option password 'jas_YOUR_TOKEN'
	option update_url 'https://[USERNAME]:[PASSWORD]@ddns.justasrv.com/nic/update?hostname=[DOMAIN]&myip=[IP]'
	option use_https '1'
	option cacert '/etc/ssl/certs'
	option ip_source 'web'
	option ip_url 'https://ddns.justasrv.com/ip'
	option interface 'wan'
	option check_interval '5'
	option check_unit 'minutes'
	option force_interval '20'
	option force_unit 'minutes'

/etc/init.d/ddns enable
/etc/init.d/ddns restart
logread -e ddns

The same fields are available in LuCI under Services › Dynamic DNS by choosing -- custom -- as the provider.

force_interval 20 minutes is the heartbeat: it keeps the host ONLINE under the default 30-minute stale threshold, and each heartbeat is a nochg on the server with no DNS write.