It depends on your objective (long)
As others have said, it really depends on what you are trying to do here. Which of the following is closer to your situation?
Scenario A:
You have a good paying job and $3K is not that much money to you in the grand scheme of things. You are OK with a small (say 5 - 10%) chance that you will lose the whole $3K on a 2-3 day trip, and if you do, then it will take you a month or two to save up another $3K and try again. You mainly just want to have some fun, and have a good chance to make some money on this one trip, and you aren't looking to make this a part time career.
Scenario B:
You have saved for a long time to get the $3K bankroll. You are willing to study and practice everything there is to know about being an AP, and you want to make this a long-term, serious hobby / second job. If you lose the $3K, it would devastate these plans because it would take you a year + to save another $3K.
My answer above assumed that you were in "Scenario B", or something similar. If you are closer to "Scenario A", then by all means go ahead and pound away at the DD games in town. I would still avoid the 6D games, but for a different reason. The DD games are more lucrative, and at your bet levels you won't need to worry about heat. I can't run the numbers right now, but I'm guessing a max bet of $150 to $200 would be about right for a sub 10% ROR over 10-15 hours of play. This should be below the radar of all but the sweatiest of casinos.
Don't get me wrong, I started out as a Scenario B guy with a BR of $1,800. Guess what I did? I didn't spend any money traveling (I was lucky to live in an area with some BJ games). I wonged shoe games, coming in with a $20 bet at any TC of +2 or greater. I scoured the local newspapers for match play and other coupons. I found BJ tourneys that had $25 buy-ins which included 2 $25 match play coupons, and an overlay. I learned how to play winning low limit Texas Hold'em ($3/$6 limit was my game of choice).
After doing this for a couple months, I won $1,000 at a BJ tourney (did I mention that I put in a ton of hours finding the tourneys with the biggest overlays?). That was an immediate 50% boost to my bankroll at the time, which allowed me to bet $30 at a TC of +2 or greater. Rinse, repeat, and get some positive variance along the way. 2-3 years later, I had a $20K bankroll and was making regular trips to Reno because the conditions were ideal for my betting level at the time. By this time, I also had sufficient BR to play the juicy DD games in my home town.
I quit playing for a while because I didn't have the BR available after life threw me some curve balls (lost jobs, kids being born, divorce). Through it all, I maintained my interest and skills, and today my BR is over $50K, and more importantly, I finally feel like I actually know how to effectively use it extract value from casinos. I have more than one tool available, which allows me to operate like a good football team. I take what the defense gives me, instead of trying to force my one and only play to work. Some casinos are vulnerable to counting. Some are vulnerable to other forms of AP. Some are vulnerable to comp / promo hustling. Some have poker rooms that attract really bad players. The key is to identify the particular casino's weakness and then attack with everything you've got.
If you want to be in it for the long-term, then focus on the long-term. What do you want your situation to be in 10-15 years? Focus on getting there. In the grand scheme, it matters not what happens next weekend.
I still remember the gut wrenching agony when I would lose 5 or more bets in a row starting out. Some of those were splits / doubles and it wasn't uncommon to lose close to $200 on a single shoe (which is a hell of alot when you've only got $2,000 to start with). I contrast that with today. The last time I played BJ, I had a $1,600 swing go against me on the turn of a single card. I had to force myself to react for cover reasons. Inside, my only thought was how odd it was that the dealer managed to pull a 5 to make 21 (and beat my 2 doubled hands of 20 each) when the true count was +10. It was a completely clinical reaction, with no emotion. I was happy that the cut card had not come out, and was contemplating how I could gracefully increase my bet after a loss, but other than that, I felt no emotion.