How can I apply the same keyframe pattern to multiple still images in Adobe Premiere? Here's what I mean by that. I'm making a short video with still images, but each one is animated Ken Burns style by gradually zooming in, or shifting position from left to right, or both. Sometimes, I'd like the motion to be diagonal as well.

My problem is that I want each animation to proceed at the same speed, but I can't find a good way to do this from one image to another. The only way I can see to make the animation is to create a keyframe at the in point, set the position or the scale, and then do the same at the out point. But it's nearly impossible to work out the right values for position or scale so that the transition from in to out happens at the same speed for one image as it does for another.

So, is there a way to create an animation by specifying the speed of the motion rather than the absolute start and end values?
Simply create your motion keyframes on your longest clip placed on your timeline (or use a dummy clip which exceeds your longest clip by a few frames or even a second in case you later add an even longer clip/image to the sequence). 

Once you have added you "start" motion position, set the keyframe, then the "end" motion position (I am guessing you will be doing pushes and pulls). 

Select the clip on the sequence. CTRL-C Copy.  Then use the C select tool (arrow) to lasso and select ALL the clips you want to apply the motion effect to. 

Right mouse click the selected clips in the sequence, then click Paste Attributes. 

This will paste the motion from your longest clip to all the clips; with the same relative speed. The keyframe for you "end" motion position on clips shorter than your "longest/dummy" clip will simply not be visible in the effects panel; because the keyframe will be out of range and past the tail of the clip. 

However, the same speed motion will be applied. 

If you are doing more than just a slow push or pull, or are dealing with various image sizes/aspect ratios; you may need to do a few "template moves" and apply the Paste Attribute command to the clips that require that specific move. 

If you need to reset the motion; select the clips on the sequence; right mouse click; remove effects; click motion, click ok. 

I would recommend also:

Run ALL your images through Image Processor using Adobe Bridge; and upres them larger than your sequence size. So if your working in a 1920x1080 workspace; use Tools; PhotoShop; Image Processor -> Resize Image (Then set a "SQUARE VALUE" of 2500 w by 2500 h).  This will box in all your images to meet either an X or Y value of 2500 px depending on the orientation of the image. 

Do not use Scale to Frame Size- as you will lose image quality on any push ins past 100%. Upresing your images using Image Processor will import all your images into PPro, and they will be larger than your sequence; so you have pull room, and push room, to go in and out, without your images pixelating. 

You may want to go higher than 2500 px. I'd recommend 2-3x your horizontal resolution. (So if 1080p, scale them all to roughly 5000/5000).  Photoshops resizing will provide much better results than PPro when moving/pushing in past 100% if your image doesnt meet your 1920 Width (if working in 1080). 

Hope this solves it for you.