Game 1 - I like your Minion plan, although there are other competitive strategies on the board and Horse Traders defends against it some. I don't agree with those saying rush for Followers, Minion can shrug off Followers no problem. I think I'd rather see a Warehouse/Minion opening over Silver. I think on turn 6 you should get Minion over Tournament, and also turn 13 I think Minion over Ironmonger. There is pseudo trashing on the board from Native Village, removing even 2-3 Estates or Coppers can really help your deck. It is also possible to control the set aside card some with Warehouse/Horse Traders/Minion discard. I'm not really sure when you should pick up a Native Village though, it's not impossible to open with it I guess. Oh, it looks like on turn 10 you have $7 and two buys so you could get it then. Maybe you can get Horse Traders on Turn 3 instead of Tournament, which will probably let you add Native Village in sooner as well.
Game 2 - Both of you have too many Crossroads too soon. I mean you trash all your Estates, the Crossroads are practically dead cards. The ideal deck here is just a bunch of Highways, Advisors, 1-2 Crossroads and then Terminals which gain you extra (or different) cards. Those terminals can be Council Room, Graverobber, Smugglers, Jester or Remake. Jester gives you the least control over what you gain so it looks like the worst. I agree with Awaclus that you take too many Oases early, at least one of those should be a Silver so you can buy a Highway. The Jester buy looks like a big mistake. Don't spend loose $2 hands on Crossroads just because you can afford it, don't add a Crossroads until your deck needs one. I am not sure about your turn 3 Smugglers, I think you want a controlled deck here and you don't have control over the Smuggler gains. It can be nice later if your opponent is taking the engine pieces you want.
Game 3 - I am not sure the Lookout is really needed, but I agree with you guys thinning a bit and building up some draw before switching to Hoard stuff.
Game 4 - It is definitely possible to build an engine here. See this log which gets 7 Provinces in 13 turns. And could have had 5 Provinces on turn 11.
http://www.gokosalvager.com/static/logprettifier.html?/20140919/log.51201cbee4b04e88c8da4f9a.1411133766109.txt I guess the key here is to get Loan and trash a lot, Journeyman and Ironmonger both give you some control over putting Coppers in the discard so you can guarantee trashing Copper. I did this once with a 5/2 start and did not get Loan soon enough and it didn't work very well. The solitaire games are misleading though, I should have realistically restricted myself to like 6 Ironmongers or something since even a money opponent is going to get some of those. If we swapped Village for Moat it would be clearly an engine. If you can draw your deck and get Horn to $8 without bending over backwards than it's definitely worth it. Speed is usually not an issue with Horn.
Jack/Candlestick Maker/Hoard should be pretty good here too. I wouldn't mix Loan with Jack, although if you're lucky and only reveal Coppers it will be good.