I know this is an old question and you have already found a solution, but for others looking at this post I'll put my two pennies worth in and suggest Enterprise Tester. It meets all of the requirements listed (see notes below) and has an API, so would allow plugins to be developed.
- Recording of test cases, including parametrised ones - Enterprise Tester allows you to record test cases and then execute those tests across one or many execution sets.
- Historical analysis of trends: number of tests, duration, success criteria - We have developed a testing query language (TQL) which allows you to analyse and report on tests (including building dashboards) within and across projects.
- Ability to "feed" test results, e.g. from automatic acceptance tests
with Selenium - Enterprise Tester can capture results from Selenium and a few other automated tools, including anything that outputs to NUnit and JUnit.
- Ability to open tasks in an issue tracker based on failed testing run - Integrates with JIRA and TFS for defect tracking.
Enterprise Tester isn't a free test management tool, but starts at $1,200 for the smallest license, so not a huge cost when price is a factor.
I hope that helps others reading this stream.
Disclosure: I work for Catch Software, the company that develops Enterprise Tester.