iCatcher! got an update yesterday that added this functionality. Now their is a download button in the top right corner of all your podcast episodes in your playlists. Just tap that button and it will start downloading to your watch. It is a bit tricky at first as tapping plays that episode, you just gotta tap the download button fast (best I can describe how to do it), just play around with it for a few minutes and you'll figure it out.
Tip: To speed up downloading turn off bluetooth on your iphone (I did it from the control center, then re-enabled it when it finished downloading). Make sure your iphone is connected to a 2.4ghz wifi network (I don't think the watch can use 5ghz networks, I have a S3 maybe the S4 or S5 can I don't know) and your download will go much faster as it is using wifi instead of bluetooth to download.
You can download episodes over cellular (however your watch has to be connected to your iphone for this to work), I can't think of anything else you could do with a cellular connection other than that (but I would love to be proved wrong! 🙂)
Wanted to take a few moments to reply to your post. Thank you for the info. Maybe that very recent update is why I love this app so much but in any case, I keep finding more to like about it. The on-watch features and level of control are second to none. Amazing what a small developer of probably one guy can do vs Apple. Imagine wanting to send a podcast episode to your watch and 2 taps later it's transferring! As simple as that!
If there is one minor complaint I have, it's the lack of ability to FULLY browse your on-phone library on your watch. For this, you are limited to using Playlists and that only shows the episodes you have downloaded, vs, say, the entire feed of a podcast which you actually can do on Apple's Podcast app. However, since episodes downloaded to the watch are so complete and controllable, I don't really see why I will need to browse my phone's Podcasts from the watch. I'll just use the phone if I am listening directly off the phone.
Regarding being able to trigger downloads as you mentioned above, that is an option I noticed but that is one of the things that only works if you use the playlists so you can actually browse downloaded podcasts on your phone and want to send them to you watch. However, if you disconnect your watch from Bluetooth, the playlists disappears, as does the ability to see that little download button.
You had mentioned disconnecting your watch from your phone by shutting off Bluetooth in control center (On the phone) but what you may not realize is doing this does not sever the connection between the watch/phone. It disconnects everything else Bluetooth related but not that connection. So basically you're watch was still downloaded from the phone. But having said that, the app is by far the fastest I've ever seen at transferring episodes to the watch. It could be because I have a series 4 watch which I think has newer (faster) Bluetooth.
I can't get the triple tap on play time to show chapters to work on the apple watch. But other than that, I couldn't love it more. I have not been this excited about an app in awhile.