there's two methods, neither is pretty.
the official method is to use the beginpolygon+polygonvertex+endpolygon builtins. 2d-mode is achieved with some flag to beginpolygon. then do your own sin+cos stuff to work out the 2d coords of the various verts and job done.
things to bear in mind:
FTE expects shader names with the argument to beginpolygon (overriding blend modes is thus considered evil, but should work).
DP expects texture names, and does not support shaders (this means you can't override things like culling, alpha masking, etc, and can't combine masks with textures or other weird and whacky stuff).
the fun method (which is excessive and isn't possible/practical in dp) is to write some glsl to do the rotation for you, however it can be a challenge compacting the info enough for it to be useful.
obviously, this method is much more work, but if you're doing weird distortion effects then this method wins.
there is no specific 'drawpicrotated' builtin. the issue is that then people would ask for a drawsubpicrotated builtin too, or something like that. you have to draw the line somewhere.
the 2d-mode of drawpolygon is meant to allow you to just generate your own damn geometry, instead of relying upon the engine for every little thing.
as a side note, 2d-mode could also be known as immediate mode as these calls go directly to the screen. note that it uses the 2d virtual size (consistant with drawpic), with depth, rather than 3d world coords.