Below are some suggestions for some contributed modules (as per your Note), for implementing some "custom search" features, and as an alternative for the "custom template" in your question.
The Forena module can be used as a custom report writer, to be considered as an alternative to "custom searches".
You could take advantage of all sorts of features related to "Report Parameters". Refer to the Users in cities assigned to a state demo report for a very basic demo of such parameters.
Demo report Master Summary with drill down illustrates how you can "link" multiple reports together (also called "drill dow reports"). To experiment with it, click on any of the (green or yellow) bars in the barchart. You'll then be forwarded to another report corresponding to the bar you selected. If you'd rather want to use the links on the tabular report below it, that's an other option you could use. By the way: Forena is not just for (tabular) reports, but also for creating charts ... (using the open source library SVG Graph, which includes support for exporting charts to PDF ...).
After you'd become familiar with its FRX-language (to develop/design reports), you have the full xHTML spectrum available. To get an idea how its Custom Queries (SQLs) and/or Report Specifications look like, refer to my answer to the question "https://drupal.stackexchange.com/questions/152166/fetching-drupal-articles-tags-image-directly-from-database/154746#154746".
And don't forget you can write your custom (native) SQL queries ... with support for SQL parameters also.
Disclosure: I'm a co-maintainer of Forena,
I hope this does not violate the site's policy on self-promotion.
By using the DataTables module for displaying Views results, and especially the "Search box" widget of it, you basically don't have to worry anymore about what exactly the users want to search for. Refer to my answer to the question "What are my options to visualise a views table with many fields grouped in columns?" for AbitMORE details about this (amazing I think) module.
Forena's integration with the DataTables jQuery plugin
Forena also has a (straight forward) integration with the DataTables plugin (no need for the DataTables module). For an illustration of it, refer to these 2 demo samples: