+1. I too had a VERY difficult time heel-toeing for quite a while, and ironically it wasn't until I actually decided to work on it at the track that it actually clicked, then I practiced it more on the street. That said, I hardly ever heel-toe on the street. Maybe it's laziness, but I just brake for a bit, let off the brake to blip a downshift if needed, and then get back to braking or just rely on the extra engine braking. But if you really want to learn on the street, here's my advice:
1. Don't expect your car's downshifts ever to sound exactly like DCT. Humans just can't blip that precisely or that quickly. Just setting expectations here.
2. Heel-toe is a bit of a misnomer for this car. Using your heel to blip the throttle is intended for cars with throttle pedals that are mounted from the top (like your brake and clutch). For floor-mounted throttle pedals like the M3's, you'll want to be braking with just the left edge of your right foot and blipping the throttle by pushing the remainder of that foot forward into the throttle, i.e. when blipping, your foot will be at an angle such that the right part of your foot is closer to the floor than the left, if that makes sense. How far you have to "roll" the right part of your foot into the throttle depends on how hard you're braking; the harder you're braking, the easier it is to blip the throttle since harder braking puts your foot closer to the floor to begin with. This is another reason why learning on the track is helpful, since most street scenarios don't have you braking anywhere near hard enough to make this easy to do, certainly not easy to learn. But if you know you're going to be heel-toeing, you have to get used to braking with only the left edge of your foot; yes, you can still brake plenty hard that way once you get used to it. The one thing you have to watch out for when you start doing that though is the risk of pressing the throttle and brake at the same time before clutching in. When I first practiced this at the track, I heard my rear brakes squealing briefly in braking zones and eventually figured out it was from me accidentally pressing the throttle while I was braking but before I was ready to downshift. The way you counter that is to actually roll your foot OUTWARD so that the right part of your foot is FARTHER from the floor than your left, which allows you to keep braking plenty hard but keeps your foot off the throttle. Of course on the street you may not have this issue since you hopefully won't be braking hard enough to push the brake pedal flush with the throttle.
3. Unless you feel that it completely messes up your throttle blip precision, start by keeping the throttle in Sport mode, i.e. Power button on. That will mean you won't have to press the throttle quite as far. I use Sport on the street and Normal on the track, but heel-toeing in Normal is definitely harder.
4. As the poster I quoted mentioned, practice on 4>3 shifts; I would say that 5>4 is probably the next easiest shift since it requires a very tiny blip. 3>2 is tough enough to get right WITHOUT heel-toe, so I'd just put that one on hold for a while because if you mess that one up you can upset your car by locking up the wheels. But practice at speeds of ~60 MPH when you've got an open STRAIGHT road with no cars behind you so they won't be bothered by your apparently pointless braking. The last thing you want is to mess up a heel-toe, get yourself and potentially your car all out of sorts, and mentally freeze up while heading into a corner. Braking with nothing but straight road in front of you and nobody around means that if you mess up, no worries. If you're wondering why I'm giving this advice given that I first practiced on the track, I started braking significantly earlier when I started this, and somehow it all just came to me pretty quickly there even though I'd never gotten it on the street -- and actually even after that track experience, getting it right on the street took some extra work given the lighter braking.
5. The shoes you wear can make a big difference. Big shoes can definitely help your foot cover the gap between the brake and throttle more effectively, but it also makes it harder to blip precisely. I bought a pair of New Balance Minimus shoes because they're fun to walk around in, and I later discovered that they make a great driving shoe. They've got a really thin sole and have that Vibram stuff but without the individual toe setup most Vibram shoes have that grosses me out.
And on a related note, I'd strongly recommend getting to the track. It sounds like you're at least partially committed to going, but I can't recommend it highly enough. Not only do you learn a lot and have a TON of fun, but you get a true understanding for why this car exists that just can't ever be discerned by M3 owners who only drive their cars on the street. Everyone talks about how different an M3 is from a 335i. Well an M3 on the track is at LEAST that big a difference from an M3 on the street -- seriously. Just decide that you're going to go and won't let anything get in your way, and it'll happen.