Yes yes yes! Go for the wrap! I think wraps are *especially* useful for older, heavier babes, as they distribute your child's weight well while keeping them snug up against you. Just make sure you go for a woven wrap, not a stretchy one, if you're wrapping an older child. This will be kinder on your back.
As a pp pointed out, there are numerous positions/wrap tricks so you can tailor your babywearing to your needs/physical comfort/kids' wiggliness. Ds loves being wrapped up with mommy, but even more than that, he also loves the wrap itself. When it's not being worn we play peek-a-boo with it, ds fiddles with the fringes (it's an Ellaroo) and sings to himself, we use it for a lap blanket in the car, we use it for an emergency changing pad, or for a "picnic" blanket if we're in a place where the floor is dirty but ds wants to get down and play or have a snack. Finally, I can wrap it around me like a big shawl or scarf and not feel silly walking around with it on when the babe isn't in it!

There *is* a learning curve, I won't kid you. You'll need to practice at home in front of the mirror (or, in my case, in front of the computer so I could refer to the directions!

), and it helps if your little one is calm and happy while you do this. (But don't worry, it won't take long before you can wrap 'em up quick, even when they're crabby!

)
And I agree with the pp who suggested going for a German wrap like a Didymos or a Storch. Ellaroos are great, too -- they're thinner, which is great for hot weather, and for wrapping ds and still being able to fit him under my coat with me -- but for your climate, I'd go for one of the others. Try German eBay -- I've seen tons of great deals there for used wraps -- like 25 euros for a Didy -- except usually the seller doesn't want to ship outside the EU. (Perfect for you!)

Good luck!