I don't know whether this will work with Rynga, but try e.g.
Voice Gateway3 -> AccessNumber -> SP2(sip.rynga.com;ui=3369950xxxx;op=ns)
Of course, substitute the actual value of the desired caller ID and the present settings for op= (if applicable).
If the above doesn't work, is it possible to move Rynga to an SPx and use a VGx for the provider currently there?
If that's not feasible, either, would Voxbeam or FlowRoute be an acceptable provider to send those calls?