That looks brilliant, my garden is enclosed with no access so I can't shift loads of soil, trying to work where I can get away with slimming the structure down that'll have the least impact on rigidity.
Looking at your design, I would at least try and get your bearers and joists to both be on posts, that alone would help the rigidity. I do think the cross bearers add a lot of rigidity, so even if you could get thinner profile wood under there it would help to minimise the bounce.
That looks brilliant, my garden is enclosed with no access so I can't shift loads of soil, trying to work where I can get away with slimming the structure down that'll have the least impact on rigidity.