I would think twice about giving your claim checks and have them get your luggage. There was a post on Facebook this week were someone’s luggage was lost this way. DME has no record of picking them up, SW had no record of where the luggage was. After 2 or 3 days, they marked it as stolen and she had to file a claim. Who knows where it went.
My last 2 or 3 trips I have picked up my luggage myself and took it to the bus. The last time I used the bag tags, it took over 7 hours for delivery. Maybe it missed the flight, who knows. My friend arrived on a different flight, her bag was delivered to the wrong room. On another trip, she was doing a split stay, her luggage was sent to her second resort, they didn’t find it for 2 days. I’d rather have it and know where it’s at.