So i've done something like this when it comes to using the transform>perspective but how do you then deal the edges of the test becoming kind of jagged from being stretched out? i've had that issue when i've even used the liquify tool.
Hmm if the jagged edges are from pixelation, you might want to make sure it's converted to a smart object first before stretching it out. You could even start it off bigger than you need, convert to a smart object, then shrink it down afterwards so it has more pixels to work with. Let me know if that helps!