I absolutely love this idea, and once I got the hang of it, the gameplay was very fun too. I write this much because I greatly enjoyed the game.
I will say that the climbing phase was very confusing at first, and I think this comes down to two factors, one major and one minor. The former is that there are two parts to most actions - choose tool, then choose target, but the game doesn't clearly show which phase you're in. One way to solve this could be to disable buttons that can't be used (so everything that isn't GO! when selecting tools and vice versa), or highlighting buttons that can be used.
The latter is that the cooldowns round down, meaning that they show 0 before they are actually ready to be used. This is a problem because in general you want to be using the items as soon as they are available, and you can't tell whether it's cooldown 0 (available) or 0 (a second from being available). This especially applies to screwdriver, which always shows 0.
Now I don't know if this game would actually be better with better balance, but I do want to note some imbalances in case you guys are interested. Among multiplicative items, big scary button is the best by a long shot, since it's both cheaper and faster and its negative is easily mitigated. Battery and overclock are both too expensive for what they do. I think the cooldown is sufficient without making them expensive as well.
Final note - on the one hand it is funny to see a long train of zeros stretching off the side of the screen. On the other hand, it would be nice to know what my score actually was. Maybe get the best of both worlds by showing both a regular number and a number in scientific notation. It's also possible to get inf/-inf/nan meters, so if you were to work on this further you'd probably want to add bignum support as well.