A lot of people seem to be getting softer bags to store theirs, but I can't bring myself to do that since I worry it'll still get dinged through the bag.
So I end up with stuff like this: https://smile.amazon.com/gp/product/B097TBKNX7/
I have a case right now that's almost exactly like that (also designed for the 351v, which I also own) but without the extra little netting in the bottom part of the case. I really like it since it feels sturdy and can fit 2-3 cartridges in the top pouch area.
It also just barely fits in my cargo pants pocket (but without the ability to close the pocket. Or easily in my shoulder bag along with my other items.
This is what I use and have no complaints.
https://www.amazon.com/gp/product/B097TBKNX7/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&psc=1
You mean RG351V right? I'm using this one: https://smile.amazon.com/gp/aw/d/B097TBKNX7
I searched Amazon up and down and found a near perfect case:
RAWECUD Hard Carrying Case for... https://www.amazon.com/dp/B097TBKNX7?ref=ppx_pop_mob_ap_share
I had to cut out the small elastic and mesh pocket on one side of the case but now my backbone fits perfectly! Leave the elastic strap in (under the controller) and it will even keep the triggers ever so slightly elevated off of the back of the case!
I've been using this one and it works great: https://smile.amazon.com/dp/B097TBKNX7