Is it necessary to run a "full node" including port forwarding in order to solo mine Bitcoin without any involvement of a pool? I see that pools are offering solo mining as an option, but why would I trust them to not take my 25 BTC? I am willing to free up 30GB for the blockchain data on my hard drive.
Are you aware how much hashing power you need to stand a chance to solo mine? In case you don't the rest of the answer is moot and you'll need to study the topic of mining some more.
Yes you'll need a full node. You don't necessarily need port-forwarding though. Full node means you validate the full blockchain and has nothing to do with network connectivity.
A full node is more like 60GB disk space at the moment and will likely be >100GB within a year.