Adding +1 Card and +1 Action together seems way too good. You said +1 Card is too strong on non-terminals, but now you are guaranteeing that the target will be non-terminal.
Getting the effects
before is easier to track. Suppose you add a token to King's Court. It's somewhat easier to count the effects as soon as you play the card rather than trying to remember to resolve it at the end of the chain. It gets even more confusing if tokens somehow get added to cards in the middle of chains, because the effects should have been locked in when the card was first played but now you might not remember what tokens were that at the beginning.
+Buy alone is sometimes weak, but not always. The idea was that an event would give you a choice of tokens, not a specific event for each token. That said, putting together +$1, +1 Buy is more reasonable than adding a full cantrip to a card.
I don't like "Gain a Silver" that much as an idea for a token, but I don't know why.
Exploration Ship -- Proper wording is "return it to the Supply".
Treacherous Swamp -- Interesting concept, but I'm unsure about the execution. This starts off as a $4 Duchy but it's near guaranteed to be worth only 2VP at the end. In most games, you can expect that your opponents will collectively gain at least 2 Provinces, thus removing both tokens from the card. So it's just a $4 2VP card in most games that sometimes costs $5 in the late game, and might be worth 3VP in exceptional circumstances. That's not that great.
Grandfather's Trail Mix -- Weird but interesting. I don't know how it would actually play out, though I expect it to be pretty weak. First play buffs Gold for the other players and hands out a Curse, but then they just bump the token down for each play. That doesn't seem like a big penalty. At the very least, you are safe for two more attacks at least. I can move the token from Gold to Silver (and have all my Silver be better than Gold!) and then later move the token from Silver to Copper.
That kind of buff to treasures makes me think that there needs to be a restriction against putting the tokens onto treasures. Or maybe the events all just need to cost more, I don't know.
As to how the tokens come into the game, it really depends on how exactly Events are implemented. Invention is fine, but you probably only buy that once a game (or twice, if you have two such tokens available). Sometimes it might be a good idea to drop the token on one card for the early game before switching to another, but I'd expect the opportunity cost to be too much; better to pick one target wisely and stick with it.
I am still following the Event model described in the OP. My idea is to have a few events that let you choose from all 10 (distinct) tokens, but with various twists. Some examples:
Ingenuity
$4 - Event
Move one of your Progress tokens in the Supply.
The straight foward one. You can add, move or remove a token. Easy. For terminology, let's say that unused tokens are "in the Supply" and it's just a question of whether they are on a card or not. If not, they simply aren't active.
Reinforcements
$3 - Event
Choose one: put a card from your hand onto your Reserve mat; or add a Progress token to a card on your Reserve mat.
In games using this, Progress token bonuses on cards on your Reserve mat act as if those cards were in the Supply.
This wording could really use some tightening up. It's a lot like the first event, but it puts the tokens on cards on your Reserve mat instead of cards in the Supply. Again, this is based on my idea that the Reserve mat turns cards into something like permanent durations that you can trigger when you want. Putting a regular (non-Reserve) card on the mat would confer that same advantage -- you can play it from the mat whenever you want, for free.
I'm not sure whether that effect alone is too good for $3. I think it should be fine; it costs you $3 and a buy to get a card onto your mat in the first place, and it only lets you take cards from your hand. That's a good deal of opportunity cost already. I think it would be OK even if this allowed you to put Victory cards on the mat, as an on-buy Island effect.
As for the Progress tokens themselves, this has some significant differences from the first event:
- you can keep the effect even if the Supply pile empties
- you lose one copy of the target card because it has to stay on your Reserve mat forever
- you have an option to play that card from the Reserve, at which point you would lose the Progress bonuses on it
The choice to put a card on the Reserve mat is there just to guarantee that there is a way for cards to get onto the mat.
Barracks
$3 - Event
Choose one: put a card from your hand onto your Reserve mat; or move 1 of your Progress tokens from the Supply onto your Reserve mat.
In games using this, trigger all Progress tokens on your Reserve mat when you play a card from the Reserve.
Instead of affecting all copies of one specific card, this event lets you give a bonus to all cards played from the Reserve. Straight forward, I think.
Provisions
$4 - Event
Move 2 of your Progress tokens from the Supply onto your Reserve mat.
In games using this, Progress tokens on your Reserve mat can be played as if they were cards, then returned to the Supply.
Again, my wording here is not great. This event uses the tokens as one-time bonuses, making them more akin to coin tokens. If there is a "+$1" Progress token, it would be almost identical to coin tokens. The difference is that this one can be spent during your action phase.
Note that if the 2 random Events are Barracks and Provisions, they would interact. Provisions lets you more efficiently put tokens onto your mat and still get the Barracks bonus.