I think I have to apologise for posing this question as I hadn't realised just much how the variance of the hunting party would cancel any advantages through play. Even though we think of the hunting party providing consistent hands, finding one of each card type in a deck, there is massive inconsistency across a series of hands. A hunting party might skip many bad cards and put them in the discard pile, or it might not and the bad cards appear in the next draw. In this scenario we simply want to avoid bad hands (not buying hunting party, not buying province) and the variance from the hunting party is too influential.
Anyway, the basic strategy was mainly covered by Captain Frisk's post. Buy one (and only one) mine. Buy hunting parties ahead of gold and the let the mine provide the wealth. There are some issues remaining, so I'll give my opinions.
Should you keep buying silvers or stop once you have enough treasure to buy hunting parties on most draws? This deck operates partially as an action driven deck and partly as a rich money deck. By the end of the game, if you draw a purchased silver instead of a hunting party you may well be able to buy a province anyway, but I'd still suggest that once you've bought two/three extra silvers you should stop. Maximise the chance of drawing hunting parties by keeping the deck smaller.
Should you mine silver-> gold or copper->silver? The main difference I see here is in mining the first gold. When you do this you add a likelihood that the hunting parties will draw the gold and reduce the chances that they draw the mine. Drawing the mine more frequently looks more attractive as it increases the gross value of the deck. However it's more important that you buy a hunting party every turn early on and the gold assures this. By the end of the game the deck is rich enough that an extra use of the mine is not missed. After the first gold I suspect you should mostly mine coppers to silvers as this reduces the chances of a bad draw where you can't play or buy hunting parties. Any hand where you draw a hunting party will nearly always be able to buy at least a hunting party that turn.
Should you remove a copper or silver entirely from your deck? Eliminating copper from the deck would be a good idea but there are not enough turns in a realistic game to make it profitable. You should certainly never remove the last silver from the deck as you don't want the hunting parties skipping past all the gold (once you have one in hand ) and leaving you short of province money. As an exception, you might want to mine your only silver to produce your only gold.
Should you take early provinces or duchies? I'd suggest that even though you have only one buy each turn, delay taking an early province or duchy. The hunting parties always find unique cards in the deck so these extra vp cards will mean that fewer productive cards are drawn each turn.
As an extra note, when playing the hunting parties you should keep an eye on the remainder of the draw deck. At times it is quite possible to deduce that by not playing a hunting party you're still assured of a good buy this turn (from the cards in hand) and a good hand next turn (from the cards still left in the deck, usually hunting parties). Playing out all the hunting parties every turn is usually good but can throw up entirely random hands for the following turn.
If anyone is interested they could consider the same scenario for a colony game.
