If there's a possibility of it happening again any time soon, don't even waste your time or all your hard work will be for nothing.
Trying to blend those scrapes in with a Dremel will probably make it worse compared to a wet EZ-Lap (DMT) diamond file or wet and dry paper and water wrapped tightly round a small wooden block. Ideally the tyres would be removed so you could run your thumb or fingers around the lip to maintain uniformity of pressure and cut.
You must maintain a straight 'cut' along the rim or it will just look dubbed over and rounded. The only way to do this properly is to weld it and reshape on a lathe, as a professional would/should so don't expect to not be able to see it if you do it by hand.
If a professional repair is out of the question and filler and paint are obviously not appropriate, your best bet is to blend the area in as widely as possible but then you're into undamaged rim and serious elbow grease usage.
The only way to effectively hide it though, is by creating as shallow a lead in and out of the gouges as possible. Using your fingertips with abrasives will follow the bumps and ruts so keep in mind that what you're trying to achieve is to take off the high spots only, as with a file.
If you do use a handfile, use a single cut draw file, cutting forwards only, lifting off to re-position at the start of each cut. Failure to do this will drag filings back over the area, scratching it badly.
This results in the removal of the bare minimum of material around the deep scratches and is much faster than wet and dry paper for the initial reshaping.
Because of the deep gouges though, I would seriously look into having it done properly with a welder to build it back up first, rather than take the surrounding rim down to the damaged level, which you'll have to do to hide it.
I haven't looked into metal aluminium fillers but I'm sure there must be a decent one available for the worst bits that will polish up.
Sanding or filing, you'll soon realise that you'd be better off filling the deepest gouges somehow, rather than trying to blend them out.