An export using previews files for a short 3:14 sequence should only take seconds not minutes if it is actually using the Preview files.
That depends on several factors. There is no 'should' other than using the previews should take less time, and in every test I've run, it does.
A true test of using Preview Files is to export in the same exact format as the Preview File render format used in the timeline so that no encoding to a new format occurs which can skew the testing.
For most of today's GOP media what you're talking about is Smart Rendering, which doesn't exist in PP on a broad basis. You get effectively the same thing with DV, and it's always been that way - DV to DV is a straight file copy when there are no changes. But I don't work with DV any more and file copy doesn't apply with most HD media. There will be a transcode process, even when preview files are used. That fact does not alter my findings.
PP is using the preview files for export.
And saying that you've done all the testing in GPU mode tells me that you really don't understand what's going on here.
I turned it off and got the same results - 3:36 for an export using the preview files.
