We leave in 3 weeks, and our two daughters who are on the tiny side, are barely tall enough and 39.5 inches tall barefoot! One is over 5.5 years old and 41 inches with shoes on. I think she's mature enough for Soarin' and I know the height requirement seems more for maturity on that one to me. 40" for Big Thunder Mountain though? I'd stick to it. KWIM? My other daughter, is 4.5 years old, and same there for her. She's definitely mature enough to sit still and enjoy Soarin' and for the life of me I can't figure out WHY it's 40" except for maturity. But, as far as other rides for 40" like Splash Mountain, I'm actually a little wary for her on that one.
Of course, going along with the being tiny in stature, they're tiny in weight departments too. The 4.5 year old weighs in at 28 pounds...thus why I'm worried about Splash Mountain and glad Big Thunder Mountain is closed.

As far as Tower of Terror...yeah RIGHT, they won't even get in line for it even if they are tall enough.
They sure are a BIG change from my first son who was 4 years old and 45 inches tall! LOL
We won't do anything to circumvent the height requirements, but our 4.5 year old will be devastated if her big sister gets to ride something and she does not. It quite terrifies me. Or course, her big sister (who is 5.5) is a little afraid of any ride that is indoors....and we had to force her on Small World the first time.
To the OP, yes, it is entirely possible your little one will grow in that amount of time.

Just prepare them for maybe not, and while I don't advocate tricks, finding a good pair of shoes that would be comfortable for the parks for all day that also happen to be thicker than say Converse shoes in the heels would be acceptable. The girls have new light up tennis shoes that they will be wearing.