You could adapt some javascript in the detail form to allow a request to be raised from an incident - looking at how the 'Create Problem' button works in 'detail_in.htmpl', for example:
<PDM_MACRO name=button Caption="Create Problem[!ea]" Func="create_new('cr',0,0,0,'PRESET=type:P','INITFROM=frm002', 'PRESET=from_incident:$args.persistent_id')" hotkey_name="Create Problem[!ea]" ID=ITIL_PROBLEM>
...from which you can see how to create a new ticket with a specific type (PRESET=type) with fields initialised from a particular form in the detail page (INITFROM=frm002), and which you could relatively easily adapt to add a button for 'Create Request'. But of course that would be an unsupported mod, and brings with it the potential to increase the effort to upgrade or apply patches, unknown implications for reporting, and so on.
Regards,
James