Where is the best centre of gravity for planes like the Berkut 360?
I cannot tell you the exact location or the locus of the CoG for the current aircraft but I can provide you a method that you can use to find the appropriate location for the aircraft to be statically and dynamically stable in flight that you can use for any future aircraft.

I'll put it simple, CoG alone means nothing, you need to know the Neutral Point (NP) of your aicraft, that is the point that if you place CoG there you'll have neutral stability (i.e. the airplane will not tend to increase or decrease a pitch up input you give with your RC). The NP is considered in practice the aft limit of your CoG.

What matters in terms of stability and control is the distance of CoG from NP that is given by what we call Static Margin (SM). An empirical rule for SM is given as

$ SM \equiv \dfrac{x_{NP}-x_{CoG}}{\bar{c}} = +0.05\ \ \ ...\ +0.15 $

where $c$ is the mean aerodynamic chord (MAC) and $x=0$ is at the leading edge of the wing's MAC.

Now, a general method to compute the NP is to use an open-source Vortex-Lattice Code like AVL of MIT (Mark Drela) (http://web.mit.edu/drela/Public/web/avl/). If you know the geometry of your airplane, and of-course you know it since you're building it, you can make the model of the airplane and with AVL you can obtain the NP from an analysis.

If you are lazy, and need an empirical and fast way to compute your NP x location then you ca.. Whoops! winglets as Vstabs... I am not sure about the validity of empirical formulas for this aircraft and you should do the algebra of flight mechanics to deduce them. It's cool but a VLM code is more general.

If you find the $x_{NP}$ you can find the $x_{CoG}$ values that satisfy longitudinal static stability criteria and then with trial and error decide what value in this range gives you the best flying experience as there is no "best" value in engineering if you don't specify the optimization constraints.

Good luck!