Hmm I wanted to post this earlier in the day before your description of the bar getting in front of you but I forgot to click Submit. So down below is my "original" post. But from you saying you can actually get your back into position because you're flexible enough, the real problem is the bar getting away from your legs. So It seems like you're just not pulling the it back into your legs hard enough. Don't forget that your shoulders will be a bit in front of the bar in the setup. That means that your arms are going to be sloped back a little (hope that's the correct term). It's visible in this picture:
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When the bar gets off the ground it wants to hang vertically from your arms and thus it gets away from your legs if you don't actively pull it back. As you're saying you can circumvent the problem with the bar getting in front of you by "squatting" the bar it's obvious that you're getting behind the it and pushing your ass down too much. This results in the shoulders being exactly over the bar and thus perfectly vertical arms. But unfortunately this leads to inefficient pulling mechanics. What you have to do is get into the correct position (as you seem to be capable of) and focus on pulling the bar back into your legs to keep it over your mid-foot.
So I'm not sure the following "original" post will be of much help now since you seem to actually be able to get into a correct setup and it's not the real issue here but there you go nonetheless:
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I also have rather short arms and thus trouble setting my back and locking it in extension. Sumo deadlifting feels really awkward to me as well, I can't even get my last conventional DL warmup weight off the floor in sumo style. Maybe I just don't use the right mechanics here but I tried it many times by now to no avail.
What I found that worked for me was to stretch/foamroll/etc. my hamstrings regularly to ensure they have their full range. Now this probably still won't be enough to be able to set your back properly with the normal deadlift setup. So what I do is to take the correct stance, start the valsalva and set my back in the correct position before bending down to grip the bar.
Now if you bend down while keeping the back locked you'll probably notice just like me that you can't even reach the bar with your hands (Hello T-Rex bro!). So what I do instead is to bend down and reach the bar with momentum while of course keeping the back locked. Once I get a hold of the bar I notice that my hamstring and everything is under a lot of tension (which is a good thing). So right then I just start the lift. Try not to wait too long or you'll run out of breath or your back will start to lose its tension, especially some reps in when fatigue is starting to set it.
The big downside of this is of course that you'll have to let go of the bar, stand up and do the process all over for each rep. Far from ideal but hey at least you can deadlift with a locked back that way. Well unless your arms are even shorter than mine and you can't reach the bar even with momentum (while keeping a locked back). In that case you're probably out of options other than doing rack pulls or having to get used to the sumo DLs if you plan to compete.