F/U interviewing while showing I got an offer

I wanted to say thank you to everyone who gave me advice on how to handle the fact that I was obviously 6 months pregnant during an in-person interview last month. As background, I had applied for a position 7 months ago, waited 5 months for a telephone interview and was then flown in for an in-person interview several weeks later. As recommended by several of you, I had a frank discussion with the HR representative about start dates at the very end of the interview day, but other than that, I kept it 100% about my skills and abilities.  This tactic worked well. Since I didn't avoid the obvious, I was able to ask for a negotiable start date which they offered me this morning.

Although I want to confirm it next week once I've had a chance to review the offer letter and packages, it seems as if the new company is happy for me to start in the fall after taking STD leave with my current employer. Therefore, my current plan is to stay at my job until the end of August, take STD with them, then when my STD ends, I'll return to my job and give my 2 to 4 weeks notice and begin with the new employer almost immediately. I'm going to look at my HR documents, but does anyone know if MD has a requirement that you need to work for 30 days after taking leave to not be obligated to repay any financial benefit? I don't want to shoot myself in the foot by doing something silly because I didn't know the rules. Although I'd love to quit now, I carry the health insurance for our family and we can't afford COBRA and a mortgage without my salary.