I am wondering if it's feasible to create a custom SOAP method that would trigger a delivery from a delivery template to the recipients whose IDs would be passed in the method as parameter (I guess a comma separated list in single parameter)?
You can use either XML format or JSON format for global parameters (or other formats but not recommended).
Then, if you don't use MessageCenter, please call the API JS method nms.delivery.SubmitNotification with a continuous delivery instead a normal or recurrent delivery and its SubmitDelivery API, in order to improve performance and management.
When you implement the custom method, you define a parameter for ID list. Either it will be a varchar and you are limited by the underlying RDBMS (such as varchar(4000) as common, or varchar(8000) and equivalent nvarchar etc).
So for storing the list value for a varchar(4000), it is 363 values that you can put, if comma separated. If it is JSON, well a bit less, and for XML lesser.
So either you split your API calls into N calls of 363 values of ID.
Or you use a TEXT / BLOB column type, that is said memo type or XML type in Adobe Campaign, it means very large (in GB) value so no problem of length for very long content as parameter (as for MessageCenter rtEvent context parameter).
Do you know perhaps what is the char limit in the parameters passed? There might be quite a bit of IDs passed there and I'm wondering if fitting them in single parameter delimited with comma is right approach.