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You don't need brute force. If you have exactly a dollar, then of course you have change for a dollar. If you have more than a dollar then you have change for a dollar except for one case, three quarters and three dimes.

Therefore, figure out the expected number of coins you draw before getting $1.00 or more; and subtract off the correction for three quarters/three dimes.

This works for the other variants as well.

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Actually, there are other situations where you have more than a dollar, but don't have exact change
1 quarter + (8-9) dimes + (0-4) pennies
3 quarters + (3-4) dimes + (0-4) pennies

Although they're not that likely to occur.
I would expect that the expected number necessay to draw 1.20 and the expected number to draw 1.00 are reasonable upper and lower bounds on that, but that really only puts you between 5 and 6 coins, which is not a particularly satsifactory answer.