Packaged web-app (so phpMyAdmin) rely on dependency from base package 'php-*'.

So you have to keep PHP base packages

phpMyAdmin in EPEL works with PHP 5.4 (base repoository), and will probably won't work with 7.2
phpMyAdmin in "remi" works with recent PHP versions, such as 7.2 from "remi-php72" repository.

SCL are mostly useful for "parallel" installation, so for multiple versions
In this case, I recommend to use the highest one (7.2 ?) as default version, and older using SCLs.

> Though.... since PHP runs on this system under PHP-FPM, it won't actually be used for phpMyAdmin, will it?

Indeed, won't be used.

> This is just a matter of keeping the RPM database consistent?

Yes

> Would it be a good idea for phpMyAdmin to change its dependencies so that have any PHP-FPM package installed would also be enough??

But this will require RPM feature not yet supported (will be in RHEL/CentOS 8 with RPM 4.14 and dnf), i.e. Rich Dependencies.

Not possible.

By design, SCL should not alter base system.
Having a common virtual provides (such ad php(http) which already exists) will create multiple providers, and thus conflicts between base and SCL packages.