Sending a CiviContribute form that's not coming from a standard donation page
There IS a viable approach to this, but I don't think it's quite what you're imagining.  Sending the form fields to CiviCRM isn't going to load the CiviContributionPage session object, where much of the data is stored.

Approaches you could take include:


Use template overrides to change the template.  It sounds like you've explored this approach.
Build the form using Webform-CiviCRM integration, which gives you much greater control over the look and feel.  This requires Drupal.
Modify the existing template's HTML after it's rendered using hook_civicrm_alterContent.
If none of these will satisfy, instead of submitting all the same form elements, instead use the Contribution API to submit your values.


Check out the Simple Donate extension as an example of folks who took the last approach.  They're using AngularJS, so the other options weren't on the table for them.