Warmest welcome to one of the greatest table tennis forum, FatCat

Its great to see that you've come to the right place. Our guys knows about inverted rubbers really well.
Also, if you haven't, why don't you introduce yourself in this thread so we could know you better. You could tell your playing style, your aptitude in table tennis so far, etc so we could help you better.
http://www.tabletennisdaily.co.uk/forum/showthread.php?12-Introduce-yourself-to-the-forum!-)
Hmm regarding bryce or H3, if you use an all wood blade, maybe you will find the H3 a tad slow, but the control is great so its good if you are a starter

I also naturally suit chinese rubber both on my forehand and backhand, maybe just like you
I haven't tried bryce but I guess the H3 will suit you. I am not completely sure though because I don't have any idea about your blade either.
Tell us what it feels like after you tried your setup will you
If you find a problem with your setup in the future, we would be glad to help. All you need to do is just ask.