When you play minions, you can actually *feel* where the critical mass is. Without trashing, all your minions do is continuously cycle your hand. This isn't a bad thing if there is some kind of +action/$ card like Pawn, Festival, etc. But without that (and this board doesn't have it), continuously cycling your deck accomplishes nothing. Infact the opportunity cost for buying your minions is just so high that you are better off spending those buys on literally anything else.
When you see minion you should look for either very strong trashing or +action/+$ cards. If neither exist, I bet you'd be surprised how underwhelming they can be. The only way you are going to get that effect on this board is if you go with Village + Vault + Minions. But then you are probably getting "too cute" for your own good, and losing to big money. That being said, I could get behind opening vault and going for a vault/village/minion engine a lot more than I can get behind a trading post transitiion to minions. TP/Minions just don't go well together.
I would be very very surprised if Trading Post/transition to minions can even remotely compete with Trading Post big money on this board. You actually don't even want that silver in your deck if you are transitioning to minions. Then, TP becomes a completly dead card. You could maybe get to critical mass, but it would take a lot more work than I'd bet it's worth. I think TP transition to big money with warehouse support for when you green would beat a minion transition every time.
And again, if you are going to force minions with a 5/2 start, I think vault/village/minions is probably miles better than Trading Post/minions.