Let's say....

[GrandMaster]

On what basis is craps better than roulette for my case?

Lower house edge.

I plugged the parameters into here:
http://www.qfit.com/blackjack-calculator-c4.htm

It's targeted towards card counters, so it's not perfect, but what the heck.
Target = 3
Starting bankroll = 2
Win Rate = -0.5 (to reflect house edge)

That gives you a risk of ruin figure. Flip that to see the odds of success. Actually, I just did it again and got 66.62.

As for the "problem" of winning more than the target amount, is that really a problem? What about ties?

I can guarantee you it is wrong. It may be based on an approximate formula which is not accurate enough for small numbers.

The probability of blackjack is at least 8/169=0.04734, so if you bet $100, you will end up with a bankroll of $350 with a probability of at least 0.04734.
Let the probability of ending up with at least $300 be x, then the player's expectation is at least 0.04734*350+(x-0.04734)*300. This can be at most 200 if the game has a house edge, hence x is at most 0.6588, but this is an overestimate, since it does not take into account the house edge, that the player won't be able to follow perfect strategy if it calls for a double after a split or for resplitting, or that the player might end with more than $300 in situations other than after getting a blackjack on the first hand.

[aka23]

The best I have come up with so far is craps. If you bet $100 on don't pass or don't come until you reach $300 or bust, you will reach $300 with probability 1826825/2779401=65.73%.

Allowing multiple bets... I am getting 65.17% for craps, assuming a 1.36% house edge on the don't pass/come bets. This is slightly above the 64.86% for single-zero roulette.

I'm getting 65.50% for baccarat, assuming a 1.06% house edge on banker.

Blackjack may be higher than any of the above, depending on specific rules and bet size. For example, with a 0.09% house edge on MG classic BJ, house edge is not going to have a tremendous effect. One solution would be to select a smaller (don't care enough to determine optimal bet size) that is a divisor of both 200 and 300, then switch to baccarat on hands where you are one bet away from busting or reaching $300.

[GrandMaster]

The best I have come up with so far is craps. If you bet $100 on don't pass or don't come until you reach $300 or bust, you will reach $300 with probability 1826825/2779401=65.73%.

I have to correct myself. I forgot about baccarat. If you bet on the player, then the probability of reaching $300 is 65.75%, assuming 8 decks.