Castor recommendation for Genesis E-330?

Since I bought a Genesis E-330 (not the new Gen-II series, but the old one) and would like to mount castors on it that allow me to better push it through my uneven backyards - what is hardly possible with the "office" like castors that come in the box:

Do you have any recommendations for good castors - both with and without brakes (I need 2 of each)?

Ideally I like to have one that looks similar to this:
My neighbor has them, but he brought them with him when moving from Europe to the US.

I've got the same problem. I keep my E-330 on a gravel-covered driveway pad adjacent to my garage. It gets a lot of afternoon sun, so during the hot summer months I'd like to wheel it over to a shady location to cook. The stock castors make this impossible because they dig in to the gravel. I haven't been able to find any suitable replacements yet. I've considered building a dolly with larger wheels and mounting the grill to it somehow. Some sort of small wheel with a pneumatic tire would be ideal (like this).

Make a dolly with larger wheels.