The resulting signed tx can be broadcast with
https://just-dice.com/pushtx, correct? Because, with a first attempt, I just got "Error: TX rejected" as reply. I think it should be possible to try broadcasting a tx with made-up data; the network would then sort them out (I used the signed tx from the example here in this thread.
Oh, and before I try with live data: The amount value is given in fractions, like 3.5 and not in the Satoshi-equivalent of 350000000 right? Not that I create a big fee

https://just-dice.com/pushtx can be used to broadcast transactions, yes.
You can use 'decoderawtransaction' to check that you have everything correct.
Values are in CLAMs not satoshis.