Hmm, with Island very slow "trashing" so I would forgo Fool's Gold, no attack so I would not spam Caravan Guard. Guess I'd go for Big Money and Mill/Tunnel, possibly open Mill/Silver, go for Mill with $4 and $5 and buy Crown later in the game.
I am no convinced of Tunnel here. You need two Mills to have better than even odds of hitting the Tunnel, and more likely three Mills. That puts you to T5/6 to get a gold. Once you have your gold in hand it is not great odds that it is better than a Silver (Mill means you aren't looking at the $1.5/card gold ... but I am guessing you have not terrible odds of drawing the Tunnel without a Mill or, as the game progresses, having 3 green in hand).
Engine-ish seems workable - Island on $4, Cgaurd/Cotr on 3 or less, Crown (early) on $5, Nobles on >=$6, and then pound the Dlands.
Honestly, I would be tempted to just run out the Dlands with mass Mills long before I would touch the Tunnels seriously. They are going to be much more effective points and you can spam them pretty easily. Maybe Tunnel/Silver, another 2 silvers, Mills/Dlands until the Dlands run out and then Tunnels.
This isn't really an accurate analysis of how you'd play Tunnel here. You don't *just buy Mills* until you hit your one Tunnel, and you certainly aren't doing the strategy to get just one Gold. You're buying like three Tunnels and many Mills, flooding your deck with Gold as much as you can get away with.
The main thing making this strategy interesting here:
1. Tunnel is the only extra gain of any kind.
2. The single-gain money variants are pretty weak (Nobles money? What?)
3. Since so much is green you'll want some extra points padding anyway over e.g. a Harem money thing.
So like, yeah you do Mill Tunnel here. The engine you're describing sounds reeeallly slow and awful with just a single gain per turn like that. I'd definitely do it if there was even like a Workshop variant or Remodel or something, but there's nothing to accelerate it. All that work for one DLands a turn? Eh.
Okay, how are you going to beat a T5/6 gold? Are we opening Tunnel? That is an odds against bet (barely) for a T3/T4 gold.
If not we open Silver/Mill, right? Okay that means T3/T4 are most likely a Mill & a Tunnel. Okay that takes us to 14 cards and two Mills. You have 12 stop cards, so 1/6 times the Tunnel is in T7. When it isn't, you have a ~2/3 shot (slightly high due to ignoring double Mill hands) at hitting a Mill with Tunnel with two Mills. Roughly, this gives you a 55% of a T5/T6 hit.
Adding in more Tunnels does help you gain more gold ... at the price of increasing the odds you have hands with no Mills for your Tunnels. Not the worse thing in Dominion, but in general slow.
Okay, so how long are we really considering for a Money build? Engine player has the option of going for Kingdom VP the whole way, so how long until you can get 8 Provs? Are you going to hit up Dlands? Duchies? If so, when? Carrying around a boatload of green, like this board seems to make likely, is going to drop your gold gaining odds. Even if you make up for a bad shuffle by having a better than average one to follow ... you still have yet another shuffle before the gold comes through.
This just seems like a slow money option for getting to 8 Provs. With Dlands, Islands, and Nobles, you really do have to plan on 8 and I am just not convinced that things are that fast.
Granted I whole heartedly concur that everything on this board is slow and the engine is also weak, but I am not seeing massive strength from the Tunnel/Mill. After all, a large part of the strength of Tunnel builds is normally being able to "win" easily at 4 Provs as your Tunnels count for a Duchy or three; after 4 prov you can just spam duchies on a normal board and cross the 50% +1 threshold without having to maintain high money density. That is just not possible here. Is the weak engine good enough to beat a slow-ish 8 Prov push?
Dunno. I just don't think it is obvious.