Okay! I figured it out and I'm very satisfied. We don't have the special tools to cut the plexigass, so we couldn't go that route. I tried the air pillows, but whenever I reached into the bag, it made scrunchy sounds. SO, I took some of your other ideas and combined it. I measure the bottom of the bag and cut a cardboard slightly larger so that I could push it to the bottom of the bag snug. Therefore, no lifting or shifting of the board. Then, I took it back out and pick up an empy black bag w/drawstrings (the one Sephora sends you your products in when you order as gift online) which had similar dimensions as my cut board (slightly larger on the sides). I put the cardboard in the bag, tied the drawstring and folded over the leftover sides to the bottom side of the board. I then inserted the whole thing to the bottom of the Speedy. And now, it has this clean, luxurious bottom w/no sagging! Yay! Thanks for all your suggestions. Wouldn't have been able to think of it w/out you!
It was pretty funny, actually. He saw me examining the bag and he asked what was bothering me. I told him I didn't want my bag to sag. Without batting an eye he said, "I can fix that in a minute." He took the bag, went into the garage, came back in a couple of minutes and it was done. Gotta LOVE DH.
Aaaah, men ARE good for something!! 
) - I measured the base of my bag, then cut three pieces out of the flaps of the box, rounded off the corners, taped the three together and placed it the bottom of the bag. Works like a charm! 
