Hmm stretchy wraps are usually really supportive, are you sure it was tied right? Normally with a stretchy you want to tie it on yourself first, don't leave space for the baby and then squish them in, as the stretch in the fabric will move to accommodate them. Very supportive then.
With buckle carriers, the idea is that the weight of the baby is transferred to your hips, so you need one which has a waistband which will sit on top of your hips. If it doesn't sit on your hips then it's going to pull on your shoulders, which will hurt your back. A useful rule of thumb with carriers is "10 minutes too tight" - you should make it just a bit uncomfortably tight to begin with, as during the course of moving around the fabric will loosen up and you'll find that it gets more comfortable. If you adjust it for comfort first, then it will loosen up as you move around and you'll find that it becomes unsupportive and feels unsafe or simply puts pressure on the wrong parts of your body.
Lastly carrying your baby facing in is the most supportive and comfortable position. If you're trying outward facing positions then these will hang the weight off your shoulders/lower back again (in any carrier).
I really like the Connecta as a buckle carrier which works reasonably well for little babies but also up to toddler age. It doesn't have as long a life span as some of them but it's a great all-rounder if that makes sense.
I haven't tried the Izmi myself, but IME those "hybrid" type carriers are often gimmicky and just don't work as well as the individual types. If you are happy with the bulk and limited sizing/uses of a buckle carrier, then stick with one of those. If you prefer the flexibility or the streamlined nature of the Mei Tai then stick with those. Trying to combine them into one and sell it as the best of both worlds usually doesn't work. For example one thing I notice immediately about the Izmi vs SSCs (soft buckle carriers) is that SSCs usually have a padded, large waistband whereas the Izmi's waistband is quite thin, and that's a really important part of an SSC in my experience.
Beware of saturation of Ergo popularity. The Ergo isn't a bad carrier but it isn't necessarily the best even though it gets loads of good reviews, it's just that it's the most accessible and well-known of all of the buckle carriers once you get beyond baby bjorn/tomy/etc (the really mainstream ones, more rigid with much more limited positioning). This can leave you with an impression that the Ergo must be amazing when really it just tends to dominate the review field because more people have heard of it. Many people who review the Ergo have never tried any other supportive carrier, and hence much of the praise heaped on "The Ergo" are comments which would apply to any soft structured carrier, which means that unless the Ergo is for some reason the only one you can possibly get, it's worth looking at a few different types of SSC.