Is it possible to have different issue types follow different workflows within a single project?
Yes, that's what "workflow schemes" are for.
A workflow scheme always has "Default - use this for all other workflows" which you can set to one workflow, then you can add other lines like "Bug uses Bug workflow, Features use Feature workflow, Improvements use Feature Workflow" etc.
check this document to get more information on how to create and configure IssueType and Workflow schemes to project
https://confluence.atlassian.com/display/JIRA/Defining+a+Project
https://confluence.atlassian.com/display/JIRA/Associating+Issue+Types+with+Projects
https://confluence.atlassian.com/display/JIRA/Activating+Workflow
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