MyEtherWallet.com has an "Advanced / Offline Transaction" tab which allows specifying a higher gas limit when making payment transactions to contracts, which is sufficient for most of the basic investment game contracts. The page is confusing the first time through, but once you understand the steps it's pretty straight forward. It would work for participating in the majority of gamified contracts being played on this forum.
So go into advanced, increase the GAS price (to what value?) then go back to basic send transaction and send to the contract?
Someone should put this in screenshots to make it easier for new people to participate.
Also, is it possible to make necessary changes to the MyEtherWallet to detect a contract address vs regular address and auto adjust the gas accordingly in the basic transaction tab?