I think you are in good shape. Here's my experience. I sell and play on all sorts of kubb sets, including the Bex set you speak of and the Tournament pieces you want to compare.
I love the rubberwood bex set you speak of, and agree it holds up better than any other commercial set I've experienced. In that regard, it's a good value.
The best "practice" you'll be getting from the set is for shooting 8 meter Kubbs. I actually use an even smaller set of Kubbs for my 8 meter practice. I use "regulation" size and weight batons, though, usually.
The Bex baton size is slightly smaller, but close enough to be "Good" practice. Baton size is one of the biggest factors affecting a "fun"game from my experience. A good balance between too light and too heavy (depnds on the person) and a good fit in the hand are the most commented on features (drawbacks) of sets I have sold. However, I believe practicing using those batons will result in better play on the bigger ones. Especially if you are paying attention to rotation, speed, etc because these motions will transfer between sizes.
Inkasting the kubbs is quite different, though, and think for the complete edge on drilling and related placement of kubbs requires not only the right size, but a matching finish on the edges. It is similar but not the same.
This brings up a difference between North American tournaments and those in Europe. Most tournament sets I have seen pictured in Europe use a routing/edging scheme similar to the Bex set you have. That is, every edge of the kubbs is rounded evenly. For tournament sets in the US, only the four long sides are rounded, and at a more extreme rounding. I believe this is a tradiition started by one of the major early US supplier of Kubb sets more than a conscious decision by any tournament to choose one style of rounding over another.
Because I hope to play in Europe soon, I have been practicing on sets that I designed and manufacture locally based on pieces from Gotland.
In all, I think you'll have a more accurate 8m and probably short baton throw by practicing on your set. Inkasting and blasting will be similar but not close enough to practice "big girl" kubb.