The multi-function shoe on the R8 is definitely more sensitive than the old 5D rails. Honestly, I noticed that same wobble with older gear. For weddings, sticking with native lighting is usually safer cuz you cant risk a misfire.

• The Canon Speedlite EL-5 fits that shoe natively.
• The Canon AD-E1 Multi-Function Shoe Adapter fixes wobble on old flashes. Godox is decent but the foot on the Godox V1-C Flash for Canon isnt always as sturdy.

Just found this and you absolutely have to grab the Godox V1-C Li-ion Round Head Flash for Canon! It is amazing on the R8 and the round head gives such a fantastic light falloff. I love how the battery lasts through an entire wedding without swapping. Since you have 350 bucks, you could even buy two! Way better value than those expensive Canon units... honestly a total steal.

I've been shooting weddings for nearly two decades now, and moving from 5D bodies to the R series was a bit of a shock to my lighting workflow. I remember being at a reception once when my old flash started misfiring just like yours... it totally kills your flow during a first dance. In my experience, Godox is basically on par with Canon TTL now, though the build feel is slightly different. Since you're looking to stay under $350 without an adapter, try these:

• Godox V1-C Flash for Canon
• This is great for weddings. The circular head gives a smoother fall-off, tho it can get warm if you're a really fast shooter.
• Godox V860III-C TTL Li-Ion Flash for Canon
• This is a total workhorse. The battery life is insane compared to the old AA days. I've found these units seat much better on the newer R8 shoes than the older legacy Canon gear does.

Seconded!

Coming back to this after seeing the other replies, I've gotta agree with Angela about the Godox performance. I've been shooting with their system for years and I'm very satisfied with the consistency. For a wedding environment where you're pushing the gear, the Godox V860III-C Speedlight for Canon is a fantastic alternative to the round-head models. It's built very well and the TTL is quite accurate on the R8. If you want the absolute latest tech within your budget, check out the Godox V1Pro-C Flash for Canon. It addresses some of the thermal issues the original V1 had during heavy use. In my experience comparing brands, Canon's native units are slightly more polished in the menus, but the Godox hardware is more than capable for professional work. No complaints about the shoe fitment on mine either... it locks down much tighter than those older legacy pins.