Here is a thinking outside of the box approach if you would consider staying at the Renaissance TA instead of the Sheraton:
Buy 4 of the 7 night Marriott certs in the forum for approximately $1,000-$1,200 total. Then convert your SPG points into Marriott at the rate of 1:3, and use 240,000 of them to upgrade the certificates to a a category 7. This way, you can have 2 rooms for 14 nights, and you can stay like a mentch instead of hiding. The approximately $1,000 out of pocket is mitigated by the 120,000 saved Marriott points.
Regarding lounge access, you would be able to bring 4 people into the lounge if you are Marriott Gold (and I imagine the baby as well), and many of the certificates for sale belong to gold accounts.