Gboard: Set Custom Unicode Characters on Longpress or Add Custom Keyboard Keys or Layout
For the time being, I found an alternative solution. It's not the solution that I wanted, but it does the job reasonably well. I'm posting it here so it may benefit someone else as well.

Gboard allows you to store a Personal Dictionary for each language that one installs (Gboard > Dictionary > Personal dictionary > English (US)). So in the keyboard in which you want to add some extra Unicode characters, add them in the Personal Dictionary of that language. With each item you add to the dictionary, you can also define a shortcut to it. So one can add ḥ — or whatever Unicode characters one needs easy access to — to one's personal dictionary and assign it a shortcut, for instance, I've assigned h key to ḥ. So whenever I press the h key on Gboard, ḥ appears in the suggestions above. 

It's not as consistent and elegant as adding ḥ to h's long-press, nevertheless, ḥ has now become much more easily accessible. The downside to this approach is that only one shortcut character can be assigned in this way to the h key, unlike the long-press option. But if you have a limited number of characters you wish to add easy access to in your Gboard, then this is an option. Though you could add other characters to a different combination of keys, like h1, h2, hdb, and so on.