However, the non-attachment preached by the Buddha conflicts with the environment around me. I'm in a large urban center in North America.
In North America & in the West, some people even treat Buddhism itself (and teaching Buddhism) as a business (for making money). I would suggest to not take to heart everything you might hear and read, because the heart of Buddhism is beyond the reach of the average person.
Achievement is valued; I feel like I'm contributing to the world in a small way.
Worldly achievement is required to earn a living or livelihood.
I feel like it makes me better at my job to dream big and get attached to goals big and small, whether it's mentoring someone junior
or committing years to a project that has an uncertain payoff.
Sure. The attitude above shows why you should not allow Buddhist theory to confuse your ordinary & natural thinking processes. Buddhism used inappropriately in the wrong contexts may lead to confusion. It is best for us to avoid getting confused & illogical. This also leads to not harming Buddhism.
This puts me at odds with my meditation practice, where "letting go" is emphasized.
Buddhist meditation is for ending suffering rather than for achieving worldly goals.
The best resource I have found specifically addressing this question is Stephen Batchelor's book "After Buddhism". In it, Batchelor lays
out one possible interpretation of the scriptures, in which the Buddha
and his disciples are very much 'in the world'---businesspeople,
merchants, town doctors, etc.---this was refreshing to read and made
me feel more at ease.
Stephen Batchelor is I think an example of what I described above; of trying to commercialise "Buddhism" in a way which harms the Buddhist teachings, by attempting to make Buddhism relevant for people that Buddhism is not actually relevant for.
Am I asking to eat my cake too? I value Buddhism and meditation, but I also value my Western individualist roots and feel egoistic
achievement is necessary for progress in science and technology.
I would suggest to simply give up any trendy aspects of your interest in Buddhism, including that book of Stephen Batchelor's.
For example, if scientists find a cure for AIDS or Cancer, there will be a great celebration in society. It will become the most trendy news. However, if this occurs, this does not mean you should take the AIDS or Cancer medicine cure if you do not have AIDS or Cancer.